How to remove paint from this window’s aluminum track

A straight razor blade shouldn't cause any trouble on your ceramic tile (assuming it has a smooth finish) or an enameled tub, but a fiberglass tub you're right to worry about.

Depending on the number of stains you're trying to remove you may find that heating the surface a bit by filling the tub with hot water then draining again will weaken their hold on the tub enough that you may be able to remove them with gentle scraping with a putty knife (being careful not to dig into the tub's surface).

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.