I am seeking advice about how to teach GO my 7y son properly. He like this game atm, playing 13x13 handicap game with me each day(he know basic rules already) but i dont know good learning methods/curve for this age category. I want to keep him attracted to game and i dont want to make any big mistakes during this process.

Ideally, find a good-level pro Go player who also happens to be a good teacher. They are rare.

Typical of this forum structure is you'll find as many different (and often opposing) ideas and replies as posters.

Don't force the child to do anything (including even good Go problems like tsumego);
rather, let him enjoy and explore Go naturally by himself.

Eventually, if this path continues long enough, you'll look for a good pro.

The Level Up books are aimed at kids, and I imagine that they can be a nice thing to support the kid. As Ed said, let the kid figure out what he likes about go and do that, but making options available (like the books, which are amusing) seems reasonable.

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Someday I want to be strong enough to earn KGS[-].

My advice would be to try hard to find kids his age he can play against.

It's very sad to me, my older daughter always had a very long attention span and enjoyed learning to play go. A local player set up a "go for kids" club and we went, and she really liked playing the other kids there. But then that folded, and she decided that she doesn't like to play me, and stopped playing. I think that if the local club had continued, then she probably would have kept playing. I made some attempt to try to set up times for her to play other kids but it just didn't really work out.

My younger daughter has a more typical attention span, which makes it harder for her to learn the game - she wants to learn to play, she'll start well, but soon her attention starts to wander so after a couple problems or 10 moves on a 9x9 game, she isn't paying attention any more and instead is just tossing down stones. Maybe some day (she is 6 now) she'll be able to learn the game but for now it doesn't seem possible.

This. In my experience children tend to play very fast, but I think that's fine, just let them do what they want to do.