How to open this paint can

Use a utility knife with a very sharp new blade and carefully cut around the perimeter of the plate at an angle as close to parallel to the wall as possible. This should get you a nice clean separation of the plate from the wall.

For the screws - if you're buying new plates they'll come with screws, and if they don't, you can find extras (including extra long ones) at your local box store.

Now as Tester pointed out, if you cannot even remove the screws, then you need a thin flathead screwdriver and a tack hammer (or a very light touch with some other hammer).

Set the head of the screwdriver against the head of the screw and lightly tap the handle with the hammer to break off the paint enough so that you can identify the actual slot in the screw. Once you have the slot identified, rotate the screwdriver so that the tip is at an angle set in the slot, and drive the tip of the screwdriver down the slot to dig out the paint.

Once you've cleaned the slot sufficiently, remove the screw as per normal use.

You will need to take off all the glue if you want a good finish.

The paint will lift the glue, but unevenly, and mix with the paint. This will cause the paint to clump and not cover properly and all in all it will look terrible.

I know because I did this in the first house I owned and had to wash the walls of the one room where I tried this several times to get as much glue off as possible. I don't think I got it completely off and you could still tell.

If you just want to paint the room, you would be better off hanging lining paper and then painting that. This has the added advantage (especially if you use 1000gsm paper) of covering any imperfections in the wall.