Guitar Touch Up Paint

I bought a used yesterday Bloody Murder Warlock guitar. It's got some scratches on it and other things.
Can I use acrylic paint to touch up the paint on it? (The paint is gone and the wood is displayed in some places)

Also, could I use a clear varnish on top of the painting?

You could, but I doubt that you would never be able to reproduce or harmonize editing to match the paint that is already there. Polyurethane is a good choice for a clear top coat. If you want a new look, remove the guitar and take the body to a repair shop auto body and spray painted professionally. You can leave it as is. Many people pay a premium for the new factory guitars are given only on a "road" look. See website Fender guitars. Some of their models look like they have been around for 30 years, scratches and all. Good luck with whatever you decide and pull a few hot licks while you think.