I log on to the laptop at school with my iserv username and password. How can I do that at home? (So, I mean, that I log on to my private laptop either with my private account or just with my Iserv account.) Is this via "Control Panel \ All Control Panel Items \ Credential Information Management" and then "Windows Credentials" → " Add Windows credentials "? If so, which server should I specify?
We can't know that. It depends on whether your school network offers the possibility to log in remotely. Since this is a security risk and the administration is not trivial, this is rather unusual. So ask the administrator in your school. You will not find a general answer here.
With iServ you can log in from home over the web or through the iServ app. With Windows login this has nothing to do outside of school.