Just take the Bishop.
Black doesn’t have to do anything in this position.
White Light Square Bishop is White’s best piece.
Black LSB is Black worst piece.
After the trade, Black position is very good.
It’s all bad for White.
In the other diagram, I would change the move order.
I wouldn’t play c5 as black to soon because White might take it and it might be there only hope to try and savage the catastrophe of their position.
Against 2. Bf5 it's starting to look better, as you say, after Ne2. I prefer an approach with Be3 to meet ...c5, rather than Ng3, which I think is premature. It;s an interesting idea but realistically only for fun, since white threw away the opening advantage with 2. e5. I would play it though, at 5 mins blitz. I will probably try it, although 1. ...e5 is less frequent than it was a month ago, when almost everyone was playing it.