I actually own a Messianic prayer book that mentions prayers for the dead.
I don't pray for the dead. I have never seen a Messianic at any congregation pray for the dead. They are in Yahshua's hands.
How common is it in Messianic Churches?
There are few Messianic congregations; as there are few Messianics.
Do you still consider yourself Jewish AND Christian?
I am a Christian, in that I follow Messiah's example. He is my Master.
If by Jewish you mean of the Tribe of Judah, no.
If by Jewish you mean a resident of Judea, no.
If by Jewish you mean Yahudim (Yah's people), yes.
Do you celebrate Christmas and Hanukkah? Baptism and Holy Communion?
I stopped honoring the Pagan ritual of giving glory to the Sun god when I was in my early 20's, long before I found others like me. Shortly thereafter I started keeping Passover, to the best of my understanding.
I don't honor Hanukkah; but most Messianics do. I think that's OK.
I do honor YHWH's Moedim (Feasts), as he commands his people to keep his Moedim forever.
I bathe. When I'm leading Moedim (feasts), I take my followers to the living waters of a river, and we take a ritual bath together giving honor to our Creator for giving us another day, another chance to repent, to have him cleanse us of any unrighteousness, and stay on the way of the narrow path to draw near to him.
In all of the Protestant churches that I attended since my earliest memories of going to church (2 years old), I never took communion. At the Messianic congregations that I have attended, we always broke bread (artos leavened) and drank grape juice in our fellowship.
I currently attend a Sunday church on Sundays. There we share communion once a month, before our fellowship meal where we bring a covered dish. once a month. The Pastor of that Church used to be Catholic, before he got deeper into the word, and became a Baptist, before he got deeper into the word, and he dropped titles other than Christian.
Shabbat Shalom
Baruk attah YHWH!