Buying "Second" Home When Primary Residence is Rental

[Jennifer Stanton]

I am currently a renter California and am looking to buy my first property in Nevada or Arizona. I plan to continue to live (most of the time) in California and spend a few weeks each year at the property in NV or AZ. 

Two questions:

Would this purchase be considered a "second home" (for tax/mortgage purposes) even though I don't own my primary residence? 

What are the disadvantages (besides no rental income) to buying a "second home" in an HOA that does not allow for rentals?