Do you know what paint he used? If it was cellulose then 2 litres, while not much, is not too bad, as he would have diluted 1:1 with thinners.
P1200 paper is great if you're confident in your technique and know there's a good depth of paint to work with. That's what I start with on the minis I paint if I get a bit of orange peel. But I paint in single stage and put down 8 + coats so I don't have to worry too much. I could also easily paint it again if I go too far.
If you suspect the paint depth on yours is not great I would start with 2500 paper and take it slowly. That's what I did on my new Zed which has a resprayed quarter panel. I use a small rubber sanding block, lots of water and a squeegee so I can see when the peel has gone. After that I use G3 paste and lots of water followed by Menzerna P2500 and P4000. All using a cheapo buffer. Mine sanded very easily so I suspect it has single stage acrylic clear coat. Two pack clear is much harder and slower to sand. It made a huge difference on mine, even improving the colour match slightly due I think to the different refraction of light in the orange peel finish to the original Nisan finish.
It's better to leave a bit of OP than go too far, especially on a white car, as it's not too noticeable.