1. No.  Consider, e.g., L=[1, 10, 2, 3].  Greedy(L) returns [1, 10],
but the longest subsequence that includes the first element from L
is [1, 2, 3].

Comments: This illustrates that greedy strategies often don't work.
Some problems are amenable to solutions with a greedy algorithm, but
many are not.  If you happen to find a problem where a greedy strategy
works, consider yourself lucky.  If you get a new problem that you
don't know how to solve, it's often still worth checking whether a
greedy strategy works, because if it does, the resulting greedy
algorithm is often very simple.  But for many problems, greedy
strategies just don't work.