Hi @Karellu,
What you've said is correct that there is damaged plaster, and the paper face of the gyprock has peeled off in sections. These are not particularly difficult things to fix, but if you had other plans in mind, fixing these issues before other steps might not be wise.
I'd need to understand what you're planning to do from here to offer the best advice possible.
Are you planning on having the taps removed? Are you planning on putting in a new laundry tub? Are you just looking to paint it, so it looks a bit nicer?
If you're removing the taps, you'd need to patch the plasterboard. Check out How to Fix a Hole in the Wall for some guidance.
For the areas where the paper has peeled away from the gyprock sheets, you'd need to skim-coat them with a topping compound such as this Gyprock Less Mess Topping Compound.
The corner also needs some work to get it back to perfect. You can use a Hyde Plasterboard Inside Corner Tool to apply the same topping compound to tidy it up.
If you can let me know some more details, I'll happily advise further.
Jacob
