It's the same in both Ancient Hebrew and Modern Hebrew:
ספר ×”×—×™×™× (Sefer ha-Chayim)
הצלחה (hatzlacha) This word is the same in both Ancient Hebrew and Modern Hebrew.
may you be inscribed in the book of life = tikatev b'sefer ha chayim (תיכתב בספר החיים)
sefer
Second life = chayim shni'im (חיים שניים)
meespareem. (if you are referring to the book of the Bible, it's got a completely different name in Hebrew: "bameedbar")
In Yiddish, "to life" is said as "l'chaim," which is commonly used as a toast meaning "to life" or "cheers."
The tree of life = etz ha-chayim (עץ החיים)
The ancient name of God, as used in the Book of Genesis, 'YHWH', is known as the tetragrammaton. Ancient Hebrew writing did not have vowels or vowel indicators, and it is sometimes difficult to determine what vowels were used in the spoken language and therefore how words were pronounced. Most scholars say that it was pronounced 'Yahweh'. This was translated into German as 'Jehovah', a word which has since entered the English language.
Ge'eh -- Ani ohev otach ge'ah. This is how you would tell a woman -- I love and respect you. Mature love. If you were writing a letter, you would say: Robin ha'ykarah for Dear Robin.
I am David = shmee dah-VEED (שמי דוד)(it's the same in both Ancient Hebrew and Modern Hebrew, only in Modern Hebrew, the name david is more likely to be stressed on the first syllable).
mateh khayyim (מטה חיים)
Moses, who was called Moshe (משה) in Hebrew.