If you are fired during your notice period, in most US states, you're still entitled to unemployment insurance for the time between when you were fired and when your notice period would end
The default standard at law is whether a reasonable person would interpret your statement as intent to resign. Generally, that means giving a specific date and not just a nebulous idea of some time in the far future. This would probably be down to a case-by-case basis. If you said "I won't be here in two weeks", that's different than "I don't see myself continuing to do this job five years from now."