Typically in my market renters want to find a place before submitting their 30 day notice so you are just lowering the vacancy.  

If so, the landlord may be choose one of these better qualified applicants over theirs, even if they may have submitted theirs first.

The house is super fairly priced, and I know I’m going to need to submit above ask, but it’ll be FHA loan so I’m worried a cash buyer will swoop in :/I’ve done some due diligence, but relatively new to all of this, so any recommendations are greatly appreciated!

I just submit a ton of offers till something bites.

It's a draft and not enforceable.Second, if it was submitted without your review, you don't have any idea what was actually submitted. 

He submitted the application for the full $3900/mo for a year lease and while I won't go into details, he was a stellar applicant with high salary and close to 800 credit score.

If it was you, the Owner, then you have every right to re-use those drawings and submit that permit as many times as you want....on your ONE building. i.e. a single time use.

Give them 72 hours to remove the unapproved animal from the property and submit to an in-person inspection to verify.

Up to 3 owners out of 6 may be unable to afford the repair, and the HOA president, as a parting gift, submitted to partial receivership to oversee the repair prior to resigning from the board. 

You do what they say and submit final photos for certification.