Labadee's beaches are as safe as they can be. Those in the little harbor are calmer. The beaches on the open side (under the zip line) can have some wave action but it is entirely up to the sea and weather conditions on that day. There are some rocks underwater so I suggest people wear water shoes.
There are chairs. There are also locals working as beach attendants who will run to get chairs for you from the stack. They expect a tip (a couple bucks). You will have to check towels out on the ship. These are not provided ashore. As always, failing to return the towels will cost you $20 per towel. They now scan your cruise card for towels - once to check them out and then again upon return.
I have no experience with the water slide.
The new pier has changed the dynamics of Labadee. People used to tender into the cove but now the action is shifted to the north end of the peninsula and the old drop-off is perhaps the most quiet section now since it takes the longest to get to. Look at my Labadee photos which are in this photo album