1. It will either be a loose wire in the power cord, or the socket in the back/side of the computer that the cord plugs into. Cords are relatively cheap to replace, most places won't repair those plugs, they'll want to replace the motherboard instead. If you are comfortable soldering on a motherboard without fear of destroying the thing, you could try to resolder it yourself.
2. This is most likely just the URL that is set as your home page. Go into Preferences/Options and change it.
3. Shotgun approach - hit it with as much stuff as you can. Install a quality Antivirus product (AVG, Kaspersky), Windows Defender, SpywareBlaster, Malwarebytes Antimalware and run ALL of them. Then reboot into Safe Mode and run ALL of them again until none of them report a problem.