Tell your mom not to bug you when you're taking a test. Keep telling her, with increasing firmness.
What does speedtest.net say? If you're sharing internet with others, they could be hogging the bandwidth. Doesn't sound like a driver issue if wired internet is slow.
Lenovo has it's own update program called System Update. Don't install 3rd party garbage to do this; they'll give you adware and junk.
Open programs and features and look through the installed programs. Use
www.shouldiremoveit.com to see which of the installed stuff needs to be removed.
School is pointless unless you have something specific in mind. Discipline will need to be learned first; something which I struggle with. I'd stay with mom as long as you can, but there's plenty of people that would disagree. Just don't let that arrangement prevent you from taking care of yourself and succeeding.