Q. My only question is do I have to pay taxes about the $3000 she will Zelle me each month somehow?
A. No.
Q. And can I claim some child care credit at the end of the year filing taxes?
A. Yes, since you are claiming the child as a dependent and the child lives with you. Your girlfriend cannot claim the dependent care credit, based on the portion she pays.
Q. Now lets say for Example I make $5000 and she gives me $3000 every month, and we spend a total of $7000 each month for our living expenses such as babysitter, rent, food, etc. then I will be spending $4000 so I will still maintain head of household from what I understand, right (her $3000 vs my $4000)?
A. No. Not based on those numbers, because the babysitter cost is not part of "the cost of maintaining a qualifying household". Include in the cost of keeping up a home expenses, such as rent, mortgage interest, real estate taxes, insurance on the home, repairs, utilities, and food eaten in the home.
References:
https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9
https://www.irs.gov/pub/irs-pdf/p17.pdf page 24
