Remove old brass tap

I will try to answer this question without seeing a picture, or knowing what exactly kind of tap you have.

Typically with an old tap that is not in good condition, it would make more sense to replace the entire thing instead of trying to replace parts on it. Plumbing fixture manufacturers are notorious for constantly changing their designs and making them incompatible with their older models.

If you can see the screws, then I am assuming there is a plastic cover over the screw. If you take a thin bladed screwdriver, or a similar tool and push it between the cover and the tap, then you may be able to pry it off.

If you are unable to remove the screw cover, then you could try using a mini hack saw to cut the cover off. Alternately, you can try using a drill to get to it. Obviously, this is a destructive approach.

Once the taps are removed, then you should be able to unscrew the fixture from below and remove the entire thing. As long as you have a standard sink, then you should be able to find an inexpensive replacement.

EDIT: It is less common, but some of the covers are the screw off type instead of pry off.

Clean off mineral deposits with a brass or steel brush and a lime dissolver such as CLR or Limewaway. Towel dry as much as possible. Dry further with hair dryer in an attempt to evaporate as much moisture as possible; this, to leave room for penetrating oil to penetrate.

Aply penetrating oil such as PB Blaster or Liquid Wrench. Tap, tap, tap the the valve to set up vibrations to encourage the penetrant. A vibrator can be useful to assist, such as an electric tooth brush or electric engraving tool. Allow penetrant to sit for hours and tap some more after that.

Use a tight fitting wrench or possibly a pipe wrench to turn it anti-clockwise.