if you get denied you cant apply again
No such restriction exists. For ANY
FFL. There ARE misdemeanors that make possession of a firearm illegal- domestic violence, and being an unlawful user of controlled drugs. If I have an indictment, I cannot get a FFL while that is "up in the air". Once resolved, that impairment goes away.
As the man said, if it is legal for you to purchase a firearm, you qualify for a FFL.
As far as firearms and probation, will depend on terms of your probation.
Now, not to be hurtful, but to be blunt- when you apply for a FFL, you are required to send a copy of the app to your local Chief Law Enforcement Officer. IF you are a dumbass that gets into trouble every time you turn around, and the bailiff at court knows your name by heart, the CLEO has the right to let the BATFE know that. Traffic tickets? No biggy. You been in court for receiving stolen property, bad checks, contributing to delinquency, theft, etc- do not expect a happy outcome.