On a conventional 30 it’s only $235/month.

I wanted to understand if any kind of debt (conventional mortgage, HELOC, cash-out refi)  on the house will be considered as COST that I spend money on rental property and they will provide me tax saving, compare to having paid-off house, in the same degree/amount. 

Go with FHA or conventional financing if the property qualifies.

I know that getting a conventional or FHA mortgages as an Independent Contractor is harder that with a W-2 job, but I would like to know, if possible: (1) How much harder it actually is(1099 x W-2)?

I'm assuming this is a rental property and based on your description you likely would not be able to get "conventional" financing....meaning, "delayed financing" would not apply here.  

Rents in the area continue to rise and home prices have had double digit growth for nearly 3 years (97405 zip code).

Rents in the area continue to rise and home prices have had double digit growth for nearly 3 years (97405 zip code).

Some could have restrictions if you want to live in the same general area, as they're probably more in the business of making long term loans, vs shorter term loans.Remember also if you want to buy two, the 1st one as owner occupied you might get away with 3-5% down conventional, but on the investment property they might want you to put down 25%. 

-Put 20% down with conventional and save over time for next investment.

The second home is my first rental using a conventional loan for an investment property.