I largely agree with your points.

Further, Kiritsugu explains his goal as eliminating master & servant simultaneously, but this seems entirely unnecessary. You should prefer to eliminate a servant first, so it can't contract with another master or act as a free agent, and also eliminate a master so they can't hang around and fight you or contract with a spare servant - but there's no need to do them simultaneously in the same battle, and with Kayneth there was even less need: he was completely crippled physically & magically, so he could neither fight nor, I think, contract again!

I think I'm going to leave this as a plot hole like in Death Note. Yes, it may be 'cool' that Near just magically deduces who Mikami is. But it's still stupid and unnecessary.