“Prepaid interest” is a thing: that means my first six months are paid and I don’t have to worry about paying for six months.

Yes it can come from the seller if the seller carries a note back, but the seller cant outright contribute proceeds towards your down payment ( closing costs and prepaid costs yes, but not DP).You'd need a lender who understands the lenders guidelines regarding a creation of a 2nd mortgage note carried back by a trust deed in CA.

You can then cash out with NO seasoning, based on the new appraised value, up to the max LTV (owner occ 80% 1-unit, 75% for 2-4 unit, and investment property 75% for 1-unit, 70% for 2-4 unit), not to exceed your initial investment, plus closing costs and prepaids. 

You'll need certified funds to go to closing or a check if it's not much and acceptable to the settlement agent.There are no points on equity loans, points are pre-paid interest.

He's also accepted a $1,300 deposit (1 point prepaid) which he refuses to return to me.

I believe you can do prepaid credit cards through your bank, but that involves paying interest on your own money or something daft iirc.As for the immigration process, it doesn't take into account credit ratings or score or bad debt from your home country.However, it does take into account criminal records and drug use.

The seller agreed to the following terms: Seller will contribute to $X towards the buyer's closing costs and/or prepaid items. 

If you have other questions just ask.The new loan amount can be no more than the actual documented amount of the borrower's initial investment in purchasing the property plus the financing of closing costs, prepaid fees, and points on the new mortgage loan (subject to the maximum LTV, CLTV, and HCLTV ratios for the cash-out transaction based on the current appraised value).

So, my counter closing date is 4/1 (if seller can collect all the rents for April which  are to be prepaid at closing).

You can buy down the rate, asmentioned above, but I rarely suggest that since it's nothing more than paying prepaid interest over the average period of time the loan is expected to be on the books, so to speak and with a commercial loan you will likely be limited to 5 years for any fixed rate anyway.