Can you play your instrument and read music after getting your eyes dilated?

Possibly. You can certainly play your instrument. Reading the music may be the issue. With dilating the eye, much ligh enters and you will be very sensitive. Focusing may be difficult and render you unable to read the music. You will not harm yourself if you try. It just will not be a pleasant experience. If you know your music, play it and "toot your horn! ".
Yes. If you are near sighted, dilating won't affect near vision as much, just will have more glare. If you are presbyopic and dilated, then using readers could help to view small print. Or could wait until dilation wears off, which is within a few hours depending on eye color.