Yes, the others have said it: notorious suggests 'bad fame' but 'notoriety' could actually be used for both bad and good sorts.

It depends on the usage, and the words that follow. If something has 'gained notoriety' with regards to something positive (teaching of modern languages), then it is a good sort of fame. "Notorious for..." is really only used to express a negative/infamy. For example "Suggustopedia was notorious for teaching languages poorly..." However, you might hear it used in comedy to express a positive because they would be opposing words: "He was notorious for being a good father."

Yes, that's a good simple definition. If someone is "notorious" they are well-known but for something that is not good, or that not everyone thinks is good. Another similar word is "infamous" which doesn't mean "not-famous" but "bad-famous" or "famous for bad".