Concerning the Christmas tree, one tradition is it that it comes from St. Boniface who chopped down a large oak held sacred by the pagans to show that the oak had no power. A fir tree sprung up where the oak was felled.
The tradition of lights on the tree comes from Martin Luther.
Not really, once you understand that when Constantine legalized Chrisitanity that hundreds of thousands of pagans converted to Christ. That the pagans exchanged gifts during their veneration of Saturn and this tradition was allowed to slip into the Christmas traditions can't be seen as a bad thing. Pope Liberius (in 354 A.D.) dedided to honor Christ as "the Light of the World" and declared His birthday to be December 25th, supplanting Saturn's veneration during this week, and this is actually a tribute to the defeat of paganism.
Christians fully understand, (or at least they should), that the important thing about Christmas is not the exchanging of gifts, or whether December 25th is the actual, precise day of Christ's birth...it's the fact that the birth of the Saviour is being celebrated all over the earth by two billion Christians that matters.