1. 2,3,6.

Explanations (which you didn't need to provide):
 1: Not necessarily.
 2: Must be true.  NP is defined to be the set of all search problems,
    and the problem statement said that FRIENDLIEST FOREST is a search
    problem.
 3: Definitely true.  The reduction gives us an algorithm for
    solving 3-COLORING, using a subroutine that solves FRIENDLIEST
    FOREST; and the total running time is at most the time the
    subroutine takes, plus polynomial time.  So if the subroutine
    only needs polynomial time, the algorithm for 3-COLORING will
    run in polynomial time as well.
 4: Not necessarily.
 5: Not necessarily.  It might be possible to solve FRIENDLIEST
    FOREST in polynomial time: this would happen, for instance,
    if P = NP, which we can't rule out.
 6: Definitely true.  Every search problem can be solved in
    exponential time: since you have a way to recognize the correct
    answer in polynomial time, just try all possibilities and you'll
    find the correct answer after trying at most exponentially
    many possibilities.

2. 1,2,3,4,5,6 -- all of them.

Explanations (which you didn't need to provide):
 1: Yeah, there might be some polynomial time algorithm
    for FRIENDLIEST FOREST, for all we know.
 2: See above; it must be true.
 3: See above; it must be true.
 4: Certainly possible.  This is equivalent to item 1.
 5: Certainly possible.  Maybe P != NP and FRIENDLIEST FOREST
    is one of the search problems that cannot be solved in polynomial
    time.
 6: See above; it must be true.

I'd also accept 1,4,5 as correct (if you thought that "could be true"
excludes everything that "must be true").