Hi, I'm not sure I'll be able to answer every question in detail, but I'll try.
1. There is always some increase in latency, but something that you can't work with. As you mentioned, I use NordVPN Teams (it's pretty much the same as regular Nord just for co-working purposes), and the latency seems to be okay. I can't comment for PIA, but I think it's okay as well.
2. From my experience, it connects quicker if the server is near to your geographical location, and longer if it's far away. But it's nothing too drastic, just wait a few seconds. And yes, you can quickly switch it off or just use it as an extension for your browser if you don't want it to be on when you are playing PC games.
3. For breaking, I haven't really experienced anything as of yet. I use Netflix with my VPN and have no problems so far. But I tend to use servers that are not the US for Netflix. I mostly use Swiss servers as they also have a huge library of media.
4. I can't really answer this question as I tend to always clean my cookies never leaving them. But I don't think you are left with the last persons settings... that would be off.
5. Don't know what else to comment on. Using a VPN is easy and shouldn't be difficult. Just pick the right provider for you, but most top-tier providers like your mentioned PIA or Nord offer really easy interfaces, so it's simple and quick to work with them as far as I've seen.
Good luck!