It can be. It's not a traditional food for the holiday like potato pancakes or jelly donuts but there is no proscription against it.
Matza isn't eaten during Purim. There is no tradition that addresses eating matza on Purim. It is treated as any other food.
Matzah; also spelled matzoh. This thin unleavened bread is eaten during Passover. See also:More about Passover and the Seder
I think you're asking about "challah". It's a Jewish bread eaten during Shabbat.
You don't cut challah, you never cut challah. It is torn and eaten. The reason is that challah is the bread of Sabbath, and a knife is an instrument of strife. In Micah 4:3, we are told that men will make plows of swords and not learn war any more in the day of the Lord. Since Shabbat is the Day of the Lord, we don't cut the bread we use on that day.
Challah is the bread that is eaten on Shabbos (Sabbath). It is customarily braided and often is glazed with egg before baking. The Challah symbolizes the Manna that the Israelites ate in the wilderness. Two loaves are placed on the table at each Shabbos meal, symbolizing the double portion of Manna (Exodus ch.16).
In addition to referring to the special egg bread eaten on Shabbat, חלה also means "to be sick".
If you're referring to the cookies eaten during Purim, they're called either Oznei Haman (Haman's ears) or Hamantashen (Haman's hat).
The sabbath is an everlasting covenant between the Jewish people and G-d. A part of its observance is to enjoy the day. Meals eaten at night, during the morning and late afternoon are all part of its observance and enjoyment.
It's challah
The same as the Sabbath and other festivals: wine, challah-bread, meat and cooked foods, etc.
Capitalize challah bread
On the Sabbath and various festivals, certain foods are eaten, such as wine (Purim and other occasions), challah bread (Sabbath), fish, especially gefilte fish, dairy (Hanukkah and Shavuoth), matzoh (Passover), apples and honey (Rosh Hashanah), fruits (Tu Bishvat), and more. If your question refers to details of keeping kosher, please see the attached Related Link.