Can my dad see my search history from his computer?

Nope. He cannot see your search history.

Just make sure you have file sharing turned off! And use your browser incognito mode....if you need privacy. The other answer are not true! If you have computers networked together...it is possible to check the files and find history and websites visited via cookies. Some people really need to read before they answer! I have been networking computers for years.

I would say if he is the administrator, has the sharing protocols, and has the software yes he can. Normally no , but download teamviewer8 and this gives you remote access, it has to be on both computers and both computers on, but you have to give permission to view.

Personally I delete history and cookies, as it will eventually slow you PC down and take up space on your drive.

Oh yes, there are a number of tools like remote desktop that would allow him to access your system remotely. You might just want to avoid doing anything on it you don't want him seeing.

No