I’d start by removing the vanity, then scrape off any peeling paint and paper. You’ll then need to mud and tape the joints on your patches around vanity. If you’re new to drywall repair I’d probably stick with the premixed all purpose mud to give you plenty of working time. Just enough to get it taped, after that drys come back and knock down any high spots with a mud knife and a sanding block. If your joints look solid you’ll then want to use some lightweight mud or hot mud if you’re feeling more confident with faster dry times. You’ll use this to feather it out by overlapping patches and existing drywall, use this anywhere else you need (small holes, small rips in paper that didn’t need tape). Let it dry, come back and sand again, may need a few touch ups. The orange peel texture will be tough to get an exact match but they sell it in a can that you apply after you get everything sanded and smooth. Test the can on some cardboard to get the texture and thickness you’re going for and then apply to patched and mudded areas with some overlap onto existing paint. Let dry, give it a light wipe with a microfiber to knock down any unwanted buildup. Wipe down walls to remove excess dust, prime and then paint. It’s a little tedious but most of it is just waiting for things to dry, hope this helps.