Hanukkah

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Yes. There are no rules about Hanukkah gifts. In fact, the only traditional gift on Hanukkah is the gelt (coins; money) given to children.

You would need to go to London or Manchester. In London, many shops in the North carry Hanukkah paper, especially Golders Green, Edgeware, and Finchley.

During the first half-hour when the candles are burning, there is a custom (not a full prohibition) to refrain from work.

Also, the light of the Hanukkah-menorah shouldn't be used for mundane purposes.

Other than that, there are no prohibitions specific to Hanukkah.

Jews

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Hanukkah is a minor holiday that commemorates the victory of the Jews against the Syrian-Greeks in the Maccabean War of 165 BCE.
The real miracle of Hanukkah is that the Jews were victorious, against all odds, they beat their enemy and were able to restore the Ancient Temple in Jerusalem, which had been desecrated by the Greeks. In a larger context, Hanukkah represents victory against religious persecution and assimilation.
But a second miracle is more commonly known: A story in the Talmud (500 years later) tells of a legendary miracle. After the war, When the Jews returned to rededicate the Ancient Temple, they found that there was only enough oil to keep the eternal lamp burning for 1 day. It would take 8 days to make more of this special oil. So the lit the lamp, and it miraculously burned for 8 days, giving them plenty of time to make more oil to keep the lamp burning.
This second miracle is very popular with children. It is understood as a legend only, and appears to be the early Rabbis' attempt to add a spiritual level to the holiday.

Answer:
The above answer is non-traditional. Our tradition is that the miracle of the oil did indeed occur and isn't just a legend. If it wasn't for the clear tradition of our Sages, Hanukkah would have been forgotten long ago. Moreover, on Hanukkah the chief celebration is not for the military victory; it's for the miracle of the oil (Talmud, Shabbat 21b). As an augmentation to the celebration of that miracle, we also thank God during Hanukkah for the Hasmoneans' miraculous military victories (during which they ousted the Seleucids and their lackeys, the Hellenizing Jews, making possible the rededication of the Temple).
The Seleucids (Syrian-Greeks) under Antiochus Epiphanes (2nd century BCE), at the instigation of the Hellenizers, had forbidden various Torah-practices in Judea, such as Sabbath-observance and circumcision, rededicated the Temple to a Greek idol, and pressed the Jews to offer up idolatrous sacrifices. Despite being heavily outnumbered, the Hasmoneans (a family of religious Jews) fought to retake the Holy Temple, which had been seized by the Seleucids, and to enable the people to once again observe the Torah. The Hasmoneans (also called Maccabees) were miraculously victorious. When they reached the Temple grounds, they immediately reconsecrated it to God. As part of this action, they relit the Menorah (Exodus ch.25), which was fueled with olive oil. However, it soon became apparent that there was only sufficient oil to keep the candelabra burning for one single day - and it would take eight days to make and bring some more.
Miraculously, the menorah stayed lit for eight days (Talmud, Shabbat 21b), allowing enough time for new oil to be prepared and brought.
The significance of the miracle is that it demonstrated that God's presence still dwelt in the Holy Temple. This is what Hanukkah represents: the closeness to God; and the avoidance of Hellenization (assimilation).
The Torah Sages instituted the festival of Hanukkah at that time (Talmud, Shabbat 21b), to publicize the miracle (Rashi commentary, ibid). This is why we light our Hanukkah-menorahs.
(The Hanukkah-menorah, or hanukkiyah, is a special form of the original seven-branched menorah. Our Hanukkah-menorahs have eight spaces for oil, or candles, to mark each of the eight days for which the oil lasted and a ninth to hold the shamash, a candle used to light the others.)
The eight-day rededication of the Temple is also mentioned in pre-Talmudic sources: Megillat Taanit (ch.9), the book of Maccabees (I, 4:56-59; and II, 1:18); and Josephus (Antiquities ch.12).
The Al-Hanisim prayer which we recite during Hanukkah centers around the Hasmoneans' victory and rededication of the Temple, while the candle-lighting commemorates the miracle of the oil.
Though the military victory is prominently mentioned in the prayers, it wouldn't have been celebrated if not for the miracle of the oil, just as we have no special occasion to mark Abraham's victory (Genesis ch.14), or those of Moses (Numbers ch.21), Joshua, Deborah (Judges ch.4), Gideon (Judges ch.6-7), Jephthah (Judges ch.11), or King David. And though the Hasmonean battles continued for two decades after the retaking of the Temple, the Sages instituted Hanukkah immediately after the miracle of the oil.
It should also be noted that the main goal for which the Maccabees fought was not political independence. They fought to enable the people to observe the Torah's commandments; as we say in the Al Hanisim prayer: "the Greeks sought to cause us to forget Your Torah and leave Your statutes."

A story in the Talmud (400 years after the Maccabean War) tells of a legendary miracle. After the war, When the Jews returned to rededicate the Ancient Temple, they found that there was only enough oil to keep the eternal lamp burning for 1 day. It would take 8 days to make more of this special oil. So they lit the lamp, and it miraculously burned for 8 days, giving them plenty of time to make more oil to keep the lamp burning.
Although this is just a legend, in modern times, we light candles to symbolize the miracle of the oil lasting 8 days.

Answer:
The above answer is non-traditional. Our tradition is that the miracle of the oil did indeed occur and isn't just a legend. If it wasn't for the clear tradition of our Sages, Hanukkah would have been forgotten long ago. Moreover, the origins of Hanukkah are spelled out both in the Talmud (Shabbat 21b) and in earlier sources as well: in Megillat Ta'anit (ch.9), which was written two centuries after the events, not 400 years. Josephus (Antiquities ch.12) mentions celebrating for eight days the re-dedication of the Temple; and the book of Maccabees (I, 4:36; and II, 1:18) mentions it still earlier.
The Seleucids (Syrian-Greeks) under Antiochus Epiphanes (2nd century BCE), at the instigation of the Hellenizers, had forbidden various Torah-practices in Judea, such as Sabbath-observance and circumcision, rededicated the Temple to a Greek idol, and pressed the Jews to offer up idolatrous sacrifices. Despite being heavily outnumbered, the Hasmoneans (a family of religious Jews) fought to retake the Holy Temple, which had been seized by the Seleucids, and to enable the people to once again observe the Torah. The Hasmoneans (also called Maccabees) were miraculously victorious. When they reached the Temple grounds, they immediately reconsecrated it to God. As part of this action, they relit the Menorah (Exodus ch.25), which was fueled with olive oil. However, it soon became apparent that there was only sufficient oil to keep the candelabra burning for one single day - and it would take eight days to make and bring some more.
Miraculously, the menorah stayed lit for eight days (Talmud, Shabbat 21b), allowing enough time for new oil to be prepared and brought.
The significance of the miracle is that it demonstrated that God's presence still dwelt in the Holy Temple. This is what Hanukkah represents: the closeness to God; and the avoidance of Hellenization (assimilation).
The Torah Sages instituted the festival of Hanukkah at that time (Talmud, Shabbat 21b), to publicize the miracle (Rashi commentary, ibid). This is why we light our Hanukkah-menorahs.
(The Hanukkah-menorah, or hanukkiyah, is a special form of the original seven-branched menorah. Our Hanukkah-menorahs have eight spaces for oil, or candles, to mark each of the eight days for which the oil lasted and a ninth to hold the shamash, a candle used to light the others.)
The Al-Hanisim prayer which we recite during Hanukkah centers around the Hasmoneans' victory and rededication of the Temple, while the candle-lighting commemorates the miracle of the oil.
Though the military victory is prominently mentioned in the prayers, it wouldn't have been celebrated if not for the miracle of the oil. It should also be noted that the main goal for which the Maccabees fought was not political independence. They fought to enable the people to observe the Torah's commandments; as we say in the Al Hanisim prayer: "the Greeks sought to cause us to forget Your Torah and leave Your statutes."

Almost every Jewish holiday begins with the lighting of candles to symbolize light (knowledge and holiness) entering the world. Another reason is practical, once the holiday begins no fires may be created so it's used to give physical light and to facilitate cooking on some holidays.

The holiday is called Channukah (Hanukkah).

Yohanan was the eldest. Judah was third.

There is only one special object associated with the holiday of Hanukkah, which is the menorah, a candelabra with 8 side branches and one central candle holder. This is one of the iconic objects of Judaism.

There was a 7-branched menorah which was lit in the Temple in Jerusalem (Exodus ch.25). After the Greeks desecrated the Temple only a small container of pure olive oil was found and this oil miraculously lasted 8 days until more could be obtained. The festival of Hanukkah commemorates this miracle and also the victory of the Maccabee rebels in their revolt against the Greeks. A special menorah (hanukkiah) with places for 8 candles (+ 1 "service" candle) is lit on each night of Hanukkah. Many people use olive oil instead of candles. After sunset (or later) one candle is lit on the first night, two on the second, etc. On Friday nights, Hanukkah candles are lit before Sabbath candles, and larger candles are used so that they will burn until after dusk for the required time.

both holidays, hang up decorations, dress up, get candy.

The same as people in America, Australia, and other countries where Jews live.

You shouldn't. Hanukkah and Christmas are no necessarily on the same day, so it would be inappropriate to wish someone a happy Hanukkah on December 25, if that day isn't during of Hanukkah.

A better idea would be to look on a calendar to see when Hanukkah falls, then then wish your Jewish friends a Happy Hanukkah on Hanukkah.

Dreidel.

No, it is not a customary Hanukkah symbol; but since it's a customary Jewish symbol, it is sometimes used in Hanukkah-themed decorations.

Usually only little children receive dreidels for Hanukkah, along with their real gifts.

They sing traditional songs and tell stories of their old days

Not very common thing to say, but it's "hyvää hanukkaa".