As far as my actual thoughts on the first hand. First off, your raised too little preflop. This likely made the flop situation worse as now you have a marginal hand in a multiway pot. As played, I would fold the flop and move on. You could very likely be behind his donking range. But also given there is multiple players seeing the flop, villain's range, and therefore your range, should be stronger than usual to bet, or continue, on this board.

If you had raised more correctly preflop, and we got the desired result of seeing a pot IP HU, then the situation changes. Now you no longer have the worry about other villains to act behind you and such. Also villains betting range, and your continuing range, should and most likely will widen. So depending on villain I could see cases for both folding to his donk bet, or calling one street. Raising would never cross my mind in this situation, and if you want clarification for why go read my above post again.