Leverage the 0% down payment, but be mindful of funding fees.

He is asking for a 25k down payment and then a 5% interest with a loan for 7 years.

I have no income as a student, but have money for a down payment.

The one caveat is that I will be unemployed during graduate school, and I will be solely surviving off of grad plus loans for tuition and mortgage payments.

But our lender is only offering us a renovation or construction loan, which I can understand.So my questions are: should we put down as much as possible to lower the monthly payment of the reno or construction loan? 

True, you didn’t have to put up the $20k, but putting up the $20k down payment and utilizing leverage increased your return by $40k, a 200% return on your $20k investment.  

From there there's typically a sliding scale pre-payment penalty.

If they are comfortable enough with my presentation i will put their invested funds towards a down payment and have the remaining balance financed by a bank.

You typically need 20% for the down payment and there are some credit score requirements as well. 

DSCR loans are based off of down payment, credit score and either actual or market rents so it helps to supercharge an investor's real estate goals and net worth.