Walls – Paint peeled off with wall border sticker

The texture difference is most likely the function of brush vs. roller. Do not thin the paint. Try using a roller, but use very litle paint on it. You are trying to get just a bit of a top coat that give the slight stippling that vitually all rollers leave behind.

Since the edges of the old paint/wallpaper are loose, you'll have to remove it back to where you get a tight edge. The main problem that you'll run into if you just try to scrape it is that you're likely to remove way to much before you get a suitable edge.

The best way that I've found to deal with paint blowouts like that is to score through the paint/wallpaper with a utility knife around the raised area, and then scrape up to your scoring. A putty knife or drywall knife works pretty well for this. This prevents you from raising more paint than you have to in order to get a decent looking repair, because the scoring will give a nice clean break in the paint.

When you have the area scraped with a clean edge, feather the edges with drywall compound and sand smooth. Since you're dealing with some sort of fiberboard instead of plaster, I'd also skim coat and sand the exposed area too (which you'll have to do anyway in order to fill the holes). After that, it should mostly disappear when re-painted.

Note that fiberboard can leech through paint pretty badly, so I'd hit it with a pretty good stain blocking primer.