I'm wondering what the standards are when it comes to pets (deposits, fees, etc), lawncare, security deposits, etc.

We have agreed to pet fee.  

I will be living in one unit, I might buy a property with conventional and bigger down payment to put down mortgage and break even or have a small cash flow and creatively think of other ways of making money through my first property like Air bnb, parking, pets, basement storage, and etcOR I can choose a different path like FHA loan and utilize the 203K Steamline or Full to fix up the house if it's a short sale or a house that needs remodeling and have a lower cost promissory note to payback and be able to cash flow with only unit and find other ways with the multi family to make money. 

That dog weighed more than some of my ex-girlfriends:) TIP: Don't allow pets in small low income apartments.

It is a two way street and I expect to do my pet as I also expect they do theirs.  

We asked to see the application, never heard back and all of a sudden it was rented and apparently this tenant has a pet.

Its possible to up the rent $1-200 per month to assume some risk (pets, month to month, ect..)To sell now and move on.

Have pets?

Finally, new tenants with pets will be paying $20 extra per month per pet, and a pet security deposit of $300.

Some HOA do not allow month to month leases, also if you want a no pet environment but HOA allows dogs and has a dog run on the premises, you can say no pets in your lease but every one who applies will be a dog owner and those who don't want pets won't be interested to rent.