Is the visit to the museum covered by some kind of tourist cards like New York Pass, New York CityPASS, e.c.t. ?

It doesn't come under the CityPass, you'd still have to pay for normal entry into MoMA if you've got that (which is $25). I know that is is included in the New York Pass though - this is a fair bit more expensive than CityPass though, so it just depends how much you're going to visit and how much you're willing to spend. It is worth shopping around for the city passes though, as there are different offers and deals with the different companies. I can definitely recommend the CityPass though - for us, it included all of the main things we wanted to do, and there were only a couple of extra things that we ended up paying for (like MoMA), but it still came to cheaper than any of the other passes, and definitely cheaper than no pass at all. Hope that helps a little! Have a great trip to NYC!

No

You might want to check out the free entry timings every Friday 4:00pm onwards for MoMA. That way you don't have to pay anything, but just make sure you go there a little early to beat the q. Also they have a baggage restriction. So if you want to save time instead of waiting in the bag checking line, carry just your camera or something. Pls visit the MoMA website for more information.