>BTW, did the QE1 have a small outdoor pool on one of its top decks?
Yes. It was added during what proved to be the final major refit. At the time, a new Lido Deck was built as well.
Whichever liner you choose, remember that location is the single greatest factor regarding success, or non-success- of a business venture. As is the impulse buy, or in the case of a tourist attraction, impulse visit. The Queen Mary, docked either in San Francisco or NYC, would benefit greatly by the latter. As it is, she is in a very bad location. NO ONE stumbles across her while doing the tourist routine. A visit to the QM requires pre-planning, and eats up the better part of a day if you add up the round trip drive plus the visit.
Also, you are going to have to find some way to make the liner generate enough money to maintain herself. That leaves the options of A) extortionate admission price, or B) partial conversion to "something else." If you want the ship left 100% intact, down to the last, smallest, third class cabin, the admission price will have to be....catastrophic.... to cover the maintenance of those 100% interchangeable, redundant, cabins that no one will ever see.
If you opt for plan B and gut the least interesting parts of the ship for conversion to "something else," then that something else has got to be SO interesting that it will draw people to the ship who normally wouldn't care to visit. Or, it has to be so INCREDIBLY interesting that people who have already paid admission to the ship will not mind paying a second admission to see this addition.
>I was wondering, isn't there a liner somewhere in Europe docked as a floating museum?
You are probably thinking of the Rotterdam, which is in the final stages of preparation for her new life as a floating hotel/historic site, in Rotterdam.
Conjecturally, it would be fun to see the Nieuw Amsterdam of 1938 magically reappear. A much more, shall we say, clever ship than the Normandie she offered not only high style but also a foreshadowing of the classless ships of the future. Cabins were fitted out by deck, not by class, so even the third class cabins on the higher decks offered private bathrooms. Subsequently, a third class deluxe cabin could be rented out on one-class cruises as a budget priced first class room, resulting in more money and zero wasted space. She was filled with the innovative small details that the Normandie singularly lacked, and was popular enough to outlive virtually all of her contemporaries. Had it not been for the fuel crisis of 1973, she might have survived long enough to warrant the sort of restoration the Rotterdam is now undergoing.