The permit application asks for a federal identification number (Fein), where do I find this? My LLC paperwork has a secretary of state file number. Is that the same thing?
The secretary of state filing may be the same as your federal EIN but probably is not. IRS Form SS-4 is how you'd apply for an EIN for your LLC. This can be done on paper or filed online. Filing for an EIN does not grant your LLC any particular tax status, it is just a number to identify your LLC to the IRS. You should review your records for a form SS-4 or the IRS letter with your EIN before applying for a new one.
You may not have or need an EIN. If you're the sole-member of your LLC and have elected to have your LLC treated as a sole-proprietorship, you don't need an EIN unless you have employees. You can use your SSN instead. If you have employees or haven't elected for your LLC to be treated as a sole-proprietorship then you do need an EIN.
Assuming you don't already have one, I'd recommend getting an EIN even if it it's not necessary for your LLC. You could use your SSN on the permit application if it is time-sensitive and then file Form SS-4 to get an EIN for future use.