Yes there is the "pay fridge" which is maintained by the cabin steward, But they are small / limited and thankfully no automatic reception billing sections on take out . The steward checks usage, bills your cabin and replaces content daily
So I would recommend
Tell your cabin steward to empty the fridge of overpriced water, soft drinks, beer etc as you do not want them.
Then bring your own on board, bottled soft drinks, water are not a problem, but remember everything goes through some sort of metal detector when you come back onboard (Airline conveyor style or personal walk through), so metal will flag. And they will question and I've seen conviscation of spirits and canned beer, to be reclaimed at the end of the cruise.
Yes they will do this, as thats how they make money, your bar tab
Glass or plastic is better, but for safety buy only brand names in ports visited.
We got our steaward to empty the fridge, so we could stock with our drinks and bottled water as I will not drink warm recycled water from the ship or pay their inflated prices for bottled