1) 8. There are 3 repeats in the 11 characters.
2) 1. The question asked how many remains, not how many remain. Remains are remnants. You shot one, so the remains of that one are in the tree.
3) Two possibilities, he is telling the truth or lying. If he was telling the truth, then the statement would be true that everything is a lie, including what he just said. This is a contradiction, so he can't be telling the truth. Can he by lying when he says everything is a lie, and it be logically possible? Yes, since not everything is a lie, but some things could be. So, of the two options, only the second is logically possible. Thus, he is lying.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue