Nail polish doesn't melt dirt. It does melt some plastics (dissolving actually). Nail polish does dissolve oils as well, and is good at loosening grunge, but so is plain water. You don't want to just cover your video card with acetone. Some of them do have a coating which might be eaten away by the acetone. I'm not sure if the actual PCB material can be hurt by it, but no sense risking it.
Primarily, just blowing it off with canned air should be sufficient to make it work well enough. If your card is overheating so badly that that doesn't fix it, then you've got more issues than just a little dust.
In this case, it sounds like the fan is dying. If you can't hear the noise while the fan is running (usually a squealing or sticking noise) then it may just be normal sounds you hear when you spin it by hand. You can clean off the blades of the fan with rubbing alcohol, as well as the heatsink. They should of course be removed from the video card to do this, or use a cloth or paper towel soaked in alcohol but not dripping. Acetone is only really necessary when you're trying to clean off stubborn thermal compound, and alcohol usually handles that well enough.
Once that's done, you can try oiling the fan. This will give it a little bit more life, but won't fix it. Peal up the label on the fan a little bit, and you should be able to see down into the hub. Just put a drop of household oil (3 in 1) onto the shaft, making sure not to get the oil on the plastic where the sticker has to go, and close it back up. The oil will help to prevent further wear, but the fact that it's already making noise means it's already damaged. You'll want to look into getting a new fan. Most current heatsinks require you to replace the whole thing if the fan fails, unless you can find a matching one. Or you could mount a regular case fan in a position to provide the airflow needed, depending on the design of the heatsink.
Clean the individual memory chips with rubbing alcohol, and do the same with the main chip if you've got the heatsink off, and if you want you can gently clean the other ICs. The heat produced by those smaller items isn't really significant though, unless you're trying to overclock to the max. Cooling the GPU is the primary issue, memory chips isn't terribly important unless overclocking. But again, the minor bit of dust that remains after using canned air isn't usually a problem. There may be a LOT of thermal compound between the heatsink and chip, not sure what the makers are using these days. When you put the heatsink back on, or a new one, only a thin layer of thermal compound should be used. The spring clips or screws should ensure that the heatsink still presses against the GPU firmly enough.
And of course, the golden rule is, if it's not crashing, it's okay. Just because the card is getting hot to touch doesn't mean it's TOO HOT. If there are no visual artifacts and no crashing, it's generally better not to touch it (although with a dying fan, you will have to eventually).