I am thinking that 12 months worth of pet rent will equal about the same as a deposit, and with pet rent, I would keep it no matter if there is damage or not, but with a deposit, I would only be able to keep it if there is damage.

You will need to keep a time log. 2.

If a partnership turns into a single member LLC due to a partner leaving, a new EIN is required but how would a business still keep the branding of their original name if creating an EIN requires a different name?

I understand you tried that and it was rejected but I think you just need to keep putting offers out there. 

If you sold it, what would you do with that money and how much income would that generate compared to keeping the house with the added costs of buying out your partners? 

Keep pressing forward!

Our current focus is working on 1-4 unit fix and flips, but eventually work towards being able to refinance properties and keep and cash flow them.My question is  tailored on the the way I should structure our relationship for the legal and tax base purposes.Should I secure the deals under my business and pay my partner out of my business operating account?

I have been using Avail for the tenant interface side of things (marketing, rent collection, etc.) and using Stessa for my accounting and record keeping.

Very New to the game i currently am about to rent out my primary home and purchase another property and hopefully keep moving up from there.

We need to earn money not keep spending it.