No government-imposed deadlines.

Therefore, unnecessary requests will be denied. 

I suggest you contact an attorney immediately.It is possible you are being set for an expensive shakedown for unnecessary monies by  professional  tenants.

Each HOA is different, so the key here is to read your By-Laws and maybe even the Declarations to find out what YOUR HOA considers to be a "Limited Column Element".What @Fred Heller said (with an unnecessary amount of snark) is essentially what is most likely to happen.  

When they try too hard, impose too many rules, it might be good for owner occupants, but really bad news for the condo landlords.

An LLC gives you limited liability without imposing double taxation on you, the way a corporation would, where the corporation is taxed and then you are taxed again when the corporation distributes profits to you.  

From a tax-deferral standpoint, it doesn't matter if you buy one property or 100 (note there are identification rules which will impose constraints on what is practical). 

Because of the Hurricane the Insurance companies will be imposing moritoriums on their agents preventing the writing of new business until the storm is past. 

From there you will narrow down your search, the bank will impose a price limit.

I don't know if the number of animals is covered, not sure if you can impose a limitation.