Understanding the Review engine

Hi

So I am struggling in the low 6xx and I did a review with a game, but despite winning, it said that my move before I checkmate was bad. So I will try to upload my last four moves/pictures.

So first I move my rock to the right. Would it have been better to move the king first, since they could make the battery, fortunately the opponent did not punish me for not doing that:

Then I move my King down, again it wants me to move it up. I think I should have move the king first, but isn't it better to move it down? I get that he can check me, but still, then I also block my plan and no defense for my rock:

In the first two moves I see that there can be some problems, but the next one I move my knight, one up to the right, why is that a bad move?: 

Then I do checkmate and suddenly it is a great move, but it is only a great move because I moved the knight or am I missing something?

Could I have done it better, smarter, faster in the last few moves? I actually expected the opponent to exchange rocks, it would have given the opponent a few more moves.  
 

Thank you, I just tried to figure out whether it was wrong or something I missed. I get your point, but it just makes it hard to fully trust the engine.

Here are your answers in the chess diagram. I advise you to put such a diagram in the future as it is much easier for you to get an answer, than a simple image. You have the option to click the miniature chessboard just above the message.

Oh and my advice is for you to try working on this yourself as well. Most of these you could have figured out on your level with the help of the engine (perhaps that line where you win a pawn is a bit more difficult), as most of your questions are answered in 2 moves or so of the engine line.

Sometimes however, things are more convoluted, and then you will surely need the help. 
In any case, you you wish to get better, analysis is crucial. And the longer time you spend on it, the better. Certainly analysis should take longer than the game itself, and sometimes much longer.

If you use the engine during the analysis, just try to be honest to yourself, if you don't understand something, that is ok, some things might be beyond your current chess knowledge, but some things you will be able to figure out if you spend some time.

Hopefully this will be helpful to you. All the best.

The “Show Moves” Button:

It has nothing to do with any battery. Your bishop is not protected sufficiently. After your move white could have taken the bishop with check, and now you're losing instead of winning.

For the second move, I’m assuming that since it is the endgame, a better move would be to centralize your king. By moving the king to the back rank, it could potentially be trapped on that rank.

I would focus mainly on the first diagram and make sure you clearly understand why your move was a mistake (drops a piece with check) as that’s a basic kind of situation that you have to get right every time if you aim to progress. The second diagram’s reason is a bit more obscure (although in general activating the king is good)

Must admit I didn’t fully understand the rest of your comments as it referred to a knight which didn’t exist.