The answer should be yes to both questions. All the ships that I've been on had very nice, roomy showers (great for those who don't fit into the cabin showers or want to avoid the dreaded shower curtain) and lockers with a key on a wristband.
I've never done it, but others report that they do it with no issues.
Not sure if there's a limit. You can just check when you board.
BTW: isn't that a lot of cash to carry around?
If you don't have one of the "plus" packages and think you might want to have one, you can use OBC to purchase after you board.
Other things you can get with OBC after you board:
Shop in one of the stores
Play slots in the casino and after several pulls (or if you're winning keep on until you lose a little), then cash out.
Go on excursions (book pre or post).
The one (and so far) only time we had the Reserve dining, there were no specials offered. I asked and was told "no". This was on the Discovery right after Covid restrictions were lifted.
When I don't get the linens that I want/request (i.e. more towels or washcloths), when I walk by a steward's cart I help myself.
Usually, a request to the steward does it, but when you get a bad one...needs must.
You don't have to sit and wait in the laundry room. The time for wash/dry are posted. Set an alarm and return to the laundry room before the cycle is complete. Rinse...repeat for the dryer.
If they're offering it...The Royal Tea has more goodies, some champagne (IIRC). Just a more upgraded affair and , yes, it costs extra.
Your niece would likely we perfectly happy with the "regular" afternoon tea and you can do it almost every day and it's included in your fare.
Try downloading "FastStone Capture" (there's a version w/a free trial). Once you have it choose "Capture Rectangle" (the button with dotted lines. Draw your rectangle around the luggage tag. Then choose print.
Probably won't be an issue for the ship. It won't look to the credit card company that you're "travelling" because the charge is from Princess...not a foreign port.
I've never seen one of those. On our Sapphire cruise last year there was a light under the desk across from the bed (inside cabin). That wasn't too bad.
The light in the picture will get taped, if we're in a cabin with one.