Is it safe to have my non gaming laptop plugged in while playing long session of games

Yes, it is safe. The laptop has circuitry in it which will prevent overcharge of the battery.

Yes and yes. The game doesn't read it as hardware and I have tried it on another laptop with the same game and it doesn't work, but it works on my mobile devices.

I have to plug it into my laptop for it to work in-game but it wont work wirelessly which is frustrating coz I bought the controller for wireless play on my laptop but I have to plug it in for it to work on my laptop but I dont have to plug it in for it to work on my laptop and phone.

See, the thing is, I don't have an option to do anything to it once I plug it into my laptop. I don't know how it could have possibly been reformatted. I plugged it into my laptop just now to try and reformat it per yours and MoeZArts suggestion
and the only option I'm given is one that allows me to "safely eject" the disk from my laptop. Plug it back into the xbox, press the option that's supposed to format for games & apps, it drops from the storage list, and I'm back at square one.

Had things going perfectly fine for the last two hours while playing Black Ops II with my fiancee and brother, and now suddenly, we can't join each others' game session. Keeps saying that the game session is no longer available.. yet we're both sitting in
a pre-game lobby. Any idea on how long this maintenance is supposed to be..?

need a better solution im not staying in the party for that long while im in a game session