Training Points (TP) do not regenerate when you are in training.
I don't know what you mean by unit limit. If you are talking about unit level limit, you can level break with Ambrosia, which you can obtain from Leana's Recycle Shop or events. If you are talking about units you can keep around, there is a skill to increase the number.
You can trade 5 level 10 3*s for 1 TE. No one buys 2*s with TE.