1 Rook Mate

This is an example of how "One rook mate" looks like.

Before I start this, Please do not complain that this i salready in chess.com. We need to pay for half of the lessons, and complte basic ones before we go in, that's why I'm here to help. 

Now Let's get into it!

First lets imagine the positions' like this:

Let's drive away the king.

We moved the rook to the left, as you can see.

How would an computer react?

Trying to attack the rook.

Let's play a waiting move.

Next move.

Let's skip a few moves.

Keep bringing the king into an "L" shape.

Next moves.

Here it is, few more moves and we are done!

Now what should we play? a waiting move!

Next move!

Almost there!

Rook under attack! Play a wating move.

L shape.

We have skipped a few moves of moving L shape.

Check!

Let's do it!

Skip till mate.

Now we got it!

Maybe with one table it would be easier

There are many weird moves in there. For example, the first move (Rf2 -> g2) is totally pointless. You should bring the king closer instead. Then there are a lot of pointless checks, letting the king get away from the edge multiple times etc. It seems to me that you only have a really vague idea of what you're doing.