So I did pay a visit to the museum and while I did not carry along any (heavy) luggage I can answer all of the questions:
- can I visit the museum with a (medium/large 55l) backpack?
I saw two guys with medium sized backpacks (ca. 30l) being asked by the guards to store them. My slightly smaller shoulder pack (ca. 20l) was fine however.
The museum has plenty of stairs and uneven terrain so if you can spare your belongings for an hour or two, I would recommend you to do so.
- alternatively can I store said backpack
Yes, there are luggage lockers in the museum square, right on your left when you enter. They look like this
and seemed spacious enough to hold even a large backpackers pack much larger than my 55l one. The locker is also very deep and can easily fit a couple of smaller backpacks. Keep a 5 zloty coin as a deposit handy.
- in case I tug along my suitcase, is there a place where I can store it?
Yes, there is a manned cloakroom right after the ticket check and entrance on your left, first room of the building and you can't miss it. By chance another visitor had a massive suitcase with her and it was stored there for her. I don't know if they charge a fee for this or ask a tip but I would be surprised if so or if it were not moderate.
Other things to take note:
Be aware the museum only opened from 10am in July and August 2016 (instead of 8am) which I somehow failed to notice on their website.