It's been a couple of years since I got my FFL, so don't remember every detail about the app process, but here's the general rundown:
Request the application.
Wait for the ATF to send it to you.
Fill out the application, get fingerprinted, write out the check for the fee and send it all in.
Wait for the ATF to process the background check and the paperwork.
Wait some more.
Call the ATF to check on your status and they'll tell you it's being processed and they'll be in contact with you.
Wait for the ATF to contact you.
Get a call from the local ATF guys to set an appointment to come to your place of business.
The ATF guys come and go over the laws and procedures with you and give you the books, starter orders of forms, information, etc. (still no license) They'll ask questions about why you want the FFL (to sell guns and make money--not for a hobby), do you have a safe/secure place to store firearms, etc.
After they leave, your application goes to another desk and you wait again.
Finally you will receive your license in the mail and are free to do business. The whole process took about 3 months when I did it.
I do not know about fixing guns without a license as I don't do repair work.
Hope that helps some, I probably left out a couple of other times of waiting for the ATF, but I'm pretty sure I got everything else in there.