Are these comics related to the video game? I thought so, seems like they are on issue 20 now. How is it? Is it part of new 52 or is it a small series that is almost over?

Yes, they take place roughly 5 years before the video game starts.

How is it? That's up for debate, but I and many others love it.

No, it's not a part of the New 52.

The writer does have an end chapter in sight eventually, but it's hopefully not anytime soon.

Yes, they're related; specifically as a prequel. It is unlikely they will catch up to the beginning of the game, however, so the events of the comics can be enjoyed without any knowledge of the game, and the game does not require reading the comics. In fact, playing the game will spoil some elements of the comics (while elucidating others). Reading the comics simply provides a deeper appreciation of some of the things in the game.

This is a self-contained series, the only universe it takes place in is the Injustice universe -- it reflects neither the old DCU nor the New 52 specifically (but it's closer to being the old, since Clark is married to Lois, Damian's alive, etc.). You'll learn very quickly (particularly in the game) that this is not at all like either real DC universe, and is absolutely outside continuity and canon.

I love it unabashedly, and try to get other people reading it. The art is generally solid and the writing is, whether you appreciate the story itself or not, absolutely fantastic; Taylor has a great grip on each character and is writing a few of them better than their current New 52 iterations.

As Gregg pointed out, Taylor (the writer) has said he knows what issue is the last one, but he hasn't actually revealed what that is.

It's worth noting that while they're on issue 20, the digital comics are only 1/2 or 1/3 the length of a print comic, so it's actually closer to being on issue 7 (and in fact they are releasing the comics in print every few weeks in combined volumes; three digital issues = one print one).

the Game itself is pretty damn good too.