The pin can be pulled out and there will be minimal flow of water. The valve and pin appear to be isolated () which explains why the main valve can stick yet the pin is free to move.
I replace the rechargeable batteries on our Gigaset phones every couple of years. I don’t think being on permanent charge does them any good. Ideally the manufacturers should have made the chargers intelligent.
I have come across a couple of random fault codes with our Vaillant boiler in the 10 years we have had ours . I would not worry about them if a reset solves them unless it happens more than once or twice.
It’s a case of finding the right installer/engineer and ideally a personal recommendation. One tip is to find a highly recommended one that is too busy and as them to recommend a local smaller company that is more likely to be available.