Is there a pass that includes travel and museums?

Now I'm reading online that April might be museum week and most museums are free?

The second week of April (8th to 14th) is Museumweek, but I wouldn't count on them having free entry. And the Museumkaart is indeed limited to 5 museums, unless you register with them to get a personalised Museumkaart.
There is a whole variety of cards for Amsterdam, some of them including public transport. The historical centre is compact (you cross it in half an hour), so I doubt very much whether you need it to get around, missing the opportunity of a nice walk in what is still a very attractive city.
With your trips to The Hague and Delft, you could consider getting the OV Chipkaart. It costs you EUR 7,50 (without the balance needed for actually paying for train, metro, bus or tram), but it makes getting around much simpler.

I will be in Amsterdam later this year. I Bought the iamsterdam card. I selected the option to pick it up on person. I printed the page with the barcode that appeared after entering my credit card and making the purchase. I have put the paper in a plastic folder I will take with me the folder also has my hostel confirmation printouts and a copy of my itinerary. The museumkaart, the one that is mainly for Dutch citizens and gives 5 museum entrances on the temporary card and unlimited entrances to about 400 sites, for a year, is not something I am getting. It looks like a waste of money and/or effort for the average tourist like us. You can’t buy the Dutch anual museumkaart until you arrive in the Netherlands, and then it has to be delivered to your hotel.