Have done multiple stays now. Others may have additional info but based on my experience...
1. They said the club is closed at least though the end of mandatory testing to return to the US. The club is currently housing the Doctors Hospital testing center (note: save yourself some time and make sure you have your Bahamian travel visa handy when getting tested).
2. Water: I use the tap and it's just fine. You can beef it up with ice from the machines. If you have full sized water bottled you can also go to the gym where there are cold filtered dispensers and fill up there. Note, the restaurants only offer still and sparking from bottles. You can also stop at the grocery on the way from the airport and pick up a case.
3. For booze, definitely stop en route to Bahamar. There are tons of well stocked liquor stores relatively close. For a few bucks the taxi should make the short stop. You can get water there too.
4. Taxi's to/fr off property restaurants start to get expensive, especially when you pay per person. Most places I've been to are in/around Nassau and too far afield to recommend unless you are already there. Poop Deck at Sandyport is good local spot. The fish fry at Arawak is a good spot where a ton of folks from the hotels and cruise ships go to eat. There are lots of options and they've added a long strong of stalls as well. Some legit jerk BBQ at the stalls. Grab a skyjuice and BBQ and sit outside-- it'll be 1/10 the price of Bahamar.
5. I'm sure its frowned upon but I'd put booze in something less obvious than a cooler--like a backpack and be covert in the pouring. Globalists get a voucher for 2 drinks for each night and these are good to use at the pool bars.
6. After 6 stays I am still puzzled by the Globalist upgrade policy. The standard upgrade seems to be a room at the next level. A fountain view upgraded to a ocean view, ocean view upgraded to ocean view balcony. Last time I had an ocean view balcony reservation I wasn't upgraded at all. A few times I asked for a suite and got one. Two great suite and one dump. It's kind of hit or miss unless you are in the Reserve. I was told on the last trip that its all dependent on inventory which I don't fully believe because inventory seemed wide open on the app. Note: front desk personnel have little to no authority to upgrade--if asked/pressed, they will go into the back and ask a manager.

Hope this help.