EVs: Yes! Short training (Weight Lift, Punch Bag and Ball Catch) gives 4 EVs. Medium (Punch Defense and Type Quiz) gives 8 EVs. Long (Block Puzzle) gives 16 EVs. If you have made the second Research and Development update, you can talk to a research and he will tell you your EVs/IVs.
LTS: No, (at least currently) you can only do local (in-game) trades.
LTS: No, (at least currently) you can only do local (in-game) trades.