I'm making my first purchase on a "non-owner occupied" duplex in Central Indiana and the first mortgage company that I went to get pre-approved will only allow 25% down.

Get your tenant to explore NON- FHA options like 99% ltv & 97% conforming loan options.Also, you need to know the REAL deal with this buyer's "Mortgage" report credit and ability to obtain a loan.  

Assisted living is very expensive, and many people stay at home where they can have home health nurses come by to administer any medically needed treatments, making it more affordable.

Are you forming a non-profit?

If you're talking a coastal SoCal duplex, the answer is probably no...it will probably not be cash flow positive (assuming a mortgage on the property).In addition to looking at non-traditional types of property, there are also some lesser populated areas of SoCal. 

When I inquire with lenders I give them the following info:Property: Investment rental (non-owner occupied SFH)Credit Score: >740Loan Amount: $80-$120KRequired LTV: 80%While im on a site like Zillow looking at properties, Ill often try to to look up rates (and APRs) and after entering in the information above  I see numbers in the mid to high 4s.

Here we have homestead exemption but as an owner non-occupant we have to pay the full tax right?

If you want primarily medical profession tenants, it will dramatically narrow down the number of buildings that would work for you. 

When used for eligible medical expenses, for example, HSA distributions are tax free.

Most beginners after their first year worry about how to deduct all their losses instead of how to reduce taxes on their (non-existent) profits.