lachagog Chayim Chadashim (לחגוג חיים חדשים)
'Chadash' (חדש) is new in Hebrew.
Second life = chayim shni'im (חיים שניים)
If you are asking how to say "Happy New Year" in Hebrew, it's shanah tovah (×©× ×” טובה)
It's the same in both Ancient Hebrew and Modern Hebrew: ספר החיים (Sefer ha-Chayim)
The tree of life = etz ha-chayim (עץ החיים)
to new friends = lechaverim chadashim (לחברים חדשים)
Matthew is not a Hebrew name, but Hebrew copies of the New Testament render it as Mah-TAH-ee (מתי).
mateh khayyim (מטה חיים)
beit khayim (בית חיים), however, this happens to be the Hebrew phrase for "cemetery".
khaverim khadashim (חברים חדשים)
shum davar khadash (שום דבר חדש)
You say 'Yalda' in Hebrew