You are only putting 5% down so your loan amount is much larger and therefore your mortgage payment.I would consider your net worth ROI.

How can my LLC get a loan?

The easiest way to initially figure out if a deal is a good deal or not (for fix and flips) is by doing the formula every lender uses to qualify a loan (70 to 75% maximum of the ARV).

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%.