We will usually comp cleaning fee or give gift cards to local restaurant to comp any legitimate issues.

As already mentioned, unless the Seller is direct family, gifting equity doesn't really work. 

If it's commercial property, active churches support bakeries, cafes, restaurants and florists/gift shops.

She’d like to gift to us somehow- is it better to sell and then gift the proceeds to invest in real estate or put the house in our name first - then we sell?  

This is often viewed as a "gift" so lenders place limits on the amount that can be "gifted" as well as the manner that these funds can be transferred to you. 

Also, with FHA, family members can give a gift to help with down payments. 

It's like getting a gift for Christmas.  

Also, if you're paying less than fair market value, you may need to be careful regarding gift taxes. 

Additionally, I can receive $40k in gifts from my father and ability to access a $20-60k loan from family at 4% APY interest.

As a non owner occupied property minimum down payments are:Conventional (single family) - 15%Conventional (multifamily 2-4 units) - 20%Non-QM (1-4 units) - 20%Certain Non-QM DSCR products allow the use of gifted funds for your down payment.