Does it work if I close on disconnected mode? or if I close my cTrader platform?
No it doesn't, the Hidden Protection only works if the cBot is running and your platform is connected to internet.
All the protection levels data are saved on your system inside a file based database.
Does it saves my settings or added protection levels?
Yes it does, if you have some open orders and you have added protection levels to those orders it the Hidden Protection will save those levels on next start.
If your orders got closed before you re-start the Hidden Protection then it will remove those levels.
Do I have to run multiple instances of it for each symbol or chart?
No you don't have to, A single running instance of "Hidden Protection" is able to manage all symbols orders.
Does it save my SL/TP levels on any remote server?
No it doesn't, your SL/TP levels are only saved on your own system.
Can I use cTrader "Advanced Protection" alongside it?
Yes you can.