Im a first time home buyer, no existing debt, self employed, bring in average $4k monthly, looking for a conventional fixed rate loan in PHX or surrounding areas.

The loan is secured by the property and I doubt the lender will release the loan unless you pay it off.

Or seek a renovation loan or personal loan from a lender?

You can do this after you close on your property just keep in mind not all loan programs allow to close or Quit claim into an LLC. 

My plan is to use the equity starting out for a profitable fix and flip or 2 then obtain another rental property,    I’m just so confused with the equity because how am I to keep being approved for the loan with having so many open?

If this is for a fix and flip your project and your level of experience will determine what type of loan you qualify for. 

I bought a 2,200sq ft 3 bed, 2.5 bath home in 2022 using the VA Loan for $330,000 at 3.25%.

We used a local credit union a few years ago to refi many of ours using conforming loans.

my wife would assume the loan, and quit claim deed her mom off.

I used my VA loan to buy a 4 plex in 2020 and still own it today, it cash flows about 2k.