I'm applying for a job. Do you think I should tell a potential employer I have asperger's syndrome?

Depends on job. If you know you are going to have trouble doing certain things such as interacting with lots of people or need to avoid too much chaos, then it might be useful to explain to your boss what those needs are to do a good job. That doesn't necessarilty require that you name your diagnosis, but sometimes that helps "explain" why you need things a certain way. Otherwise, no.
No. It is really nobodies business. I would not tell my employer.