Vandalism would normally be covered by comprehensive coverage, and won't affect your premiums; you'll just have to pay a deductible. If you tried to do it yourself, you'd never get the paint to match quite right, so you're better off taking it to an auto body shop to have it professionally repaired.

Depends, how much do you care, and how good does your car still look?
If you drive a pristine car that you plan on selling eventually: get it done at a bodyshop.
If you drive an older car or plan to keep it until it dies, and dont care about the looks too much: chrisfix has some good videos on working with a paint pen

If you drive a 20 year old car in the rust belt: lol

If you're in the the US, file a police report. If for anything documentation (and local crime statistics). I'm sure there won't be any real investigation, but it does help identify patterns.

Also, when/if you choose to file an insurance claim, you'll have a police report number. Which may or may not help grease the wheels of the claim.

I wouldnt bother with ChrisFix when it is about paintwork, after i saw his videos on bodywork i lost all trust in his skills concerning that. AmmoNYC (irrc) has an old video featuring a Mercedes g-class where he shows different ways to do it, from "i just dont want it to rust" to "only the best is good enough".

If when you run a fingernail over it, if your nail catches in the scratch, the scratch is very likely too deep to fix with paint correction(like buffing/polishing).

A proper fix will require prep, painting and blending, which you shouldn't try to do yourself. You could buy a touch up stick that matches your paint to cover the scratch. It won't look perfect and won't last forever without clear coat on top, but it will prevent rust.

Before you decide how you'll deal with this, you can bring it to a body shop for an estimate, most shops will do that for free. Most shops can give you an estimate from photos emailed or submitted to their websites.

If you're just worried about rust I'd say do it yourself it's not that hard

How deep is the scratch?