Here are a few tips to help you with your rental situation:1. 

I am interested in adding a 264 sq feet space in my front yard, attached to the main home for rental purpose.

This is not a financial planning question but a simple can you afford to buy a home and how much can you afford if you can buy.You might have better luck posting in the home buying section of this site as this personal finance portion of BP doesn't get much attention.

Does Texas allow home equity sharing loans (also called equity investment loans)? 

I also suspect home prices would initially rise on the first 1-1.5% of cuts, but ultimately fall once we get to the 3-4% range as large  pre-pandemic supply comes back online, compounded by boomer land lords selling realizing the top of the market is in the rear view mirror (at least for them).If you eventually get squeezed on lower rents and valuations as the market normalizes, the ability to BRRR your pandemic era deals will be limited, so how do avoid trapping capital in the deals you already own from this environment? 

@Joey B. the main benefit to using FHA is that your are able to purchase a home with minimal down payment.

Eat at home.

Should i use part of a home equity loan to put a down payment on another house to rent out? 

Been doing my due diligence to find some homes in the Raleigh area that are pre-foreclosured on as well as foreclosed.

Flat and shallow correction in median home prices.