After you hire someone you go to the 'Reception tab', to the right of their image there should be a "serve" button, if not then their obedience is to low for the clients, so click "Next day" until the "serve" button appears.
ThatBrothelGame_Data/StreamingAssets/Saves (most likely, haven't tested to confirm, just found it and a file in there)
1) Yes. 2) Yes, if you load the game there is a discord button on the main screen that should take you to it. 3) Not sure, but I've seen a couple updates of packs in the last 2 months on the discord.
I noticed the same, seems different characters have different obedience growth rates, you just have to experiment until you find the ones that go up fast and then use them at the start of your games. Maybe one of the new items increases the speed it increases? but I haven't looked to see.
After you buy a item go into the Reception tab and then right click on the picture of your girl, can "apply item". There is a tread mill in the store for 30k that says it helps build up stamina, so maybe there is a way to increase arousal max too.