And is it normal practice for Lender to change their language like that?

What language should I look for on contract to secure my money?

I think the agent is a little incompetent, it’s not a counter offer, it would be a disclosure, or a correction/clarification even if it had to be added to the language of the contract. 

No assignments of contract, no resale or mtg for 90 days after your closing for more than 120% of your purchase price, plus other typical REO language.

In that scenario your investment could be at risk if you aren't able to make it cashflow after paying for all expenses including property management.As a former US Marine, active real estate investor, licensed CA agent and property manager I'm able to speak your language and can help you avoid extremely costly mistakes. 

@Bradley Jordan My recommendation is that you ask the 2nd broker to write in specific language that covers your situation.

Should I have him add language to the promissory note that I am paid out first upon sale of the property?

Many HOAs have language around rentals in their docs.

AirBNB specifically recommends language pertaining to allergies and service animals - you can state in your listing that you don't accept any animals (don't say "pets") due to allergies and it being a health risk to you or a family member.Again, definitely look into the laws yourself, but between this being your primary residence, your only STR, and you having allergies, I don't believe you could be required to accommodate service animals.

Have an attorney review the language of any contract you are signing/being assigned, to look for potential traps.