Building a Fortress

I recently completed a tournament in Navalmoral de la Mata (Spain) where I finished with 7.0/9. My only loss of the event was to the top seed, GM Sergey Fedorchuk, in the 3rd round (Fedorchuk coasted to first place with 7.5/9). The game featured a lot of strange material allocations in the middlegame that had both of us wondering who was playing to win. The questions continued into the endgame where a number of theoretical endgames could have arisen. I have looked at a few such endgames endgames (like Q vs 2 minor pieces and Q vs R + pawn), and while they didn't actually arise during the game, you'll see that they easily could have occurred in the notes. In the end though, under severe time pressure, I failed to build a fortress and he won the endgame.

Question 1: What would you play as Black after 14.Qe2?

Question 2: What would you play as Black after 28.Ba2?

Question 3: What piece would you take here as White - the bishop on a2 or the knight on d6?

Question 4: What is White's basic strategy to win this endgame?

Even though I lost this game, I wasn't too disappointed with the result. It was a complicated fight with lots of interesting moments to look at. Here's the entire game in one viewer: