Some places limit the amount you can charge.

For the deposit your location may play a role but where I live there is no limit to the deposit you can take outside of the market. 

Preferably a traditional side by side duplex or triplex or a property that would allow an Airbnb with a private entrance (not a rent by the room fan).I’m not looking to buy until the next 8-12 months and know the current multi-family supply is quite limited making it even more of a challenge.

As an example, no jurisdiction can demand a minimum lot size, limit your max size below 850sf, or limit the square footage beyond the states laws, etc.

Now, maybe they said something different and it was lost in translation a bit but here's the things to keep in mind when buying with cash and using Fannie/Freddie loans.The "Cash Out" limit is 75% for single family homes and 70% for 2-4 units NO MATTER WHAT. 

A dual disclosed agent, in NJ anyway, now works for both so it limits the agents responsibilities (or increases depending on your point of view). 

These loans are usually to an LLC not a person, you wont be limited to how many you can hold.   

Questions-Is buying a home first going to limit my ability to buy a rental?

Personally, I like to limit my rehabs to ~20-30% of my purchase price to limit risk. 

Is the HOA able to enforce this, is there a statute of limitations?