My duplex has gained about $50K in equity and I'm wondering if I should use that equity towards purchasing another property?

Hopefully you can gain access and get the property cleaned up.

how much do I owe for capital gains for fed and state?

When the taxpayers demolished their existing principal residence, built a new home on the land, and sold it before ever occupying it, the Tax Court ruled the gain resulting from the sale of the never-occupied home did not qualify for exclusion under IRC Sec. 121 (Court case: Gates).

Also, this home along with my other rental is depreciated, that means my real estate company, on paper nets zero dollars..... so unto $80,700 worth of stock market capital gains and dividends - are taxed at a 0% rate.  

After renting out my old home for almost 6 years, I am considering selling it now and curious about capital gain taxes as the house is now worth about $450,000.

(3) if we were to pull the trigger on this, we would likely want to do a Section 121 to preserve our equity gains, as much as possible, and pour it back towards the downpayment of the multi-family.

I see a great one in the mirror behind my set of free weights.

You've got a great situation in that you can sell your primary residence side and take the gain tax free. 

That would kill solar heat gain from windows.But if you haven't switched the vents for summer, yeah, that's normal.