Second homes cannot be utilized for DSCR loans because they can't produce income to qualify.

For a SFH there typically needs to at least be some sort of equity and if not, then the debt to income needs to be strong.

Assuming I could qualify financially (primary income plus FHA allowed rental income contribution from additional leased units), when I become the owner of the property, would that prevent me from using a FHA 203b to house hack a second property?

Every investor’s goals, resources, and strategy are different, and there is no one-size-fits all solution to market finding.You’ll walk out understanding:How to balance your goals for cash flow and appreciationWhy home prices don’t paint the whole picture for affordabilityHow metrics like the rent-to-income and rent-to-price ratios are similar (and how they aren’t!)

Should I agree to this so I can make some additional income, or is this opening a can of worms that I don't want to open? 

All the benefits of living near CA but no state income tax.

The data the city requested was more than would be reflected on my income taxes. 

If they provide you one, I would still say I am getting my own.I would ask for full demographics of the area, including incomes, home prices, education levels, crime levels, etc.I would want to see full tenant application and any pertinent backup verifying income, employment history, landlord references, etc of the in-place tenant.I would want to talk to the property manager, if they are coming with the property.  

These type of loans have the least requirements and are usually approved based on the investment property alone and not the income of the borrower.The highest interest rates will be from a hard money lender.

I haven't seen this lately but be careful and read the terms - there are often terms in the mortgage that preclude using the second home as an income property or limit the number of days you can be paid rent on it.