In about 90 minutes you see everything, but I suggest to go in early morning...inside no air condition...

Not a formal cloakroom. There is a guardhouse-like structure before the entrance ramp. I saw them direct a backpacker to leave hers there. However, I didn't see that this room was being continuously occupied by staff. Vietnam is generally safer than most places on the USA. But as an ex-New Yorker, I'm rather cautious in situations like this. We both entered the museum with day packs. So maybe you could use a compromise strategy where you segregate valuables and essentials into a discreet backpack and leave the rest at the guardhouse? I guess it depends whether your stowed luggage is modest and you're only traveling with a limited wardrobe so you wouldn't be devastated if you lose it.

Opening the door from 8:00 to 11h30 . 14h to 17h

The souvenir shop seemed pretty good and the replica statues seemed to be good quality. I must admit to not looking that closely but it had good selection.

The entrance fee is 40 000 VND per adult, children may be cheaper I think

Every day of the week

Walk along side of Han River toward the Golden Dragon bridge. There is an underground walkway just before you get to the bridge, then cross the road to the museum. Hope this helps