When George shoots Lennie is this a sign of strength of Georges love or the weakness of his love? Has George finally followed through on the threat to abandon Lennie? Why does George shoot Lennie in the middle of their imagining the farm one last time?

This is probably best understood as open to interpretation. It is very possible to read George's final action as a way of liberating Lennie from the coldness that is his life full of unfulfilled desires. On the other hand, it could be read as George "giving up" on his best friend.

Like Roskolnikov states above, this question is definitely open to interpretation. I see George's final action as an act of love and strength. Lenny has escaped his determined fate before with George's help; what George liberates him from is death by the hands of people who don't understand, men who won't try to understand. George understands that this is the end, Lenny is going to be executed, and he is guilty of a crime whether he's mentally aware of it or not. George takes on the responsibility out of love. Lenny's death is quick, instantaneous, and it's performed while Lenny is imagining the farm which is his 'one' happy dream.