OneNote Logout and Sign-up bound to Email?

My OneNote is bound to my email address, right?

Say when I give my laptop for repair, everything is deleted and then I get a new one, my OneNote is still included in itself because I can log in again via the ACC - right?

Depends on whether you use O365 or not. The notebooks would need to be on a server to keep them. In general, you can see where these files are. If you go to File in OneNote, you should see under Information where your notebook is. Does it somewhere on C: then it is not synchronized. Therefore, you should best secure this on a USB stick.