Are quotes only for spoken text? Can I use quotes to emphasize sarcasm, like when somebody physically makes quote symbols with their fingers while reading?
I've only seen people make quote symbols with their fingers while speaking, not reading. If someone's speaking, you already have a set of quotes, you'd have to alternate between single and double quotes to keep them apart.
Sure, works for me. If you want to know for certain, consult a style guide like the Chicago Manual of Style (only available to subscribers, alas).
Yes, you can absolutely use quotes to indicate sarcasm (or irony).
If the sarcasm is in dialogue, you can write it exactly as in Hobbes's example. If you want to have the additional stage business of the speaker making air quotes, you can do that too, but most readers will understand what the sarcastic quote marks mean.
If the sarcasm is in prose, you would use double quotes in the same manner.