You're doing great, this is just the process :). If you used a standard wood glue, you'd be best off sanding it as it's more durable than the drywall that it's bonded to. You can try some vinegar and a plastic scraper but just be sure not to dig into the wall.

If you want to sand it, you can buy what looks like foam rectangle blocks at the hardware store that has the abrasive built onto it's edges. They're pretty handy to keep around the house for projects. Once you get as much off as you're able, you can fill any divits or dimples with the putty I mentioned prior then either sand or wipe with a wet cloth.

If it's wood glue, you're in trouble. It has likely bonded to the paint and it will be necessary to remove the paint and glue together. If you really want to do this right, get a painters 5 in 1 tool and scrape it off, then sand, patch, and prime, and repaint.

Generally, stuff doesn't get glued to walls. Wood glue is for gluing untreated wood to other untreated wood.

The brackets, and their size/length hold up the weight of the shelf and its contents.

good work so far! dont give up :)

Schwim Dandy is giving good advice here. If it were me, I'd take down the shelf, spackle and sand the wall a bit with one of those foam sanding blocks, use painter's masking tape to make a frame around the area on the wall, paint the area inside the frame of tape some darker color, then put the shelf back up. The shelf will look nice on the rectangle of paint and everything will look clean.

These anchors are pretty amazing. I highly recommend them. Nothing beats fastening to a stud but these are fantastic in a pinch