...Nxc3 has been played by GMs in these positions. I don't think the "loss of tempo" is significant as White isn't going to do anything with it anyway.
5...e6 weakens the dark squares and shuts in Black's light-squared bishop. I don't think this move can be played.
5...Nb6 is normal.
I do not really understand your point. There are several reasons why Nxc3 is not a bad move and I explained these reasons all in previous posts. I also explained that by moving his knight and then exchanging it is not bad in this position. Black might have lost a tempo but in this positions that is not a problem