The inspector contacts me and lets me know that he wasn't able to find permits for that edition.

The reason was their basement work was un permitted work which did not agree with city code.

If you feel they have been doing a poor job you can absolutely fire them (contract permitting) you might go with a different PM company though instead of trying to manage yourself from 10 hours away. 

I was considering drawing the plans myself and submitting them to acquire a permit.

It's your first deal, you don't have a contracting network, you don't have an architect, you've likely never go through a permitting process, if 4-plexes are impossible to find it might have to do with restrictive zoning, etc.  

You don't need to be G.C to manage, most city's allow Owner/Builder to pull permits and hire subs.

All notices required or permitted under this Agreement shall be in writing and shall be deemed delivered when delivered in person or deposited in the United States mail, postage prepaid, addressed as follows:IF for The Seller and/or The Buyer:___________________________________________________________________________Address: ___________________________________________________________________Print: _______________________________________ Date: ___________________________IF for The Consultant:___________________________________________________________________________Address: ___________________________________________________________________Print: _______________________________________ Date:___________________________Such address may be changed from time to time by either party by providing written notice to the other in the manner set forth above. 11.

If I were starting out I'd just buy a residence I could afford and in two years (while the laws still permit) just fix it up slowily and sell for tax free gain.

The land has permits to build an additional 5 duplexes.

So, certain parts of Florida are a nightmare with permits.