Hi,
No, In Afghanistan we do not put up any kind of tree for eid.. The day is started by waking up early and going to the masjid for prayer, and we wear our best clothes, and spend most of the day visiting relatives and celebrating.
No, you do not have to put up a tree at Christmas. It's your choice whether to have a tree or not.
It's up to you really. We put ours up a couple of weeks before Christmas day but some people like to put up their decorations earlier.
You put it up to honor Jesus, for Santa clause to put presents under, and to remind you of Christmas!
http://www.answers.com/topic/christmas-tree
Day after Thanksgiving or...whenever you want...seriously people, there are no rules here