[Robk]

as a general comment it seems that youre being too formulaic in your thinking. even if you learn the "right" answers to these questions, using that strategy wont get you that big of an edge. you need to tailor your play to the exact situation at hand to get a big edge at shorthanded poker.

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1. When you're playing 4-6 handed and are in the BB, what unpaired hands are worth 3 betting against a non-steal raise? I usually have been 3betting any hand I feel has equity against his range, but I feel that some of my 3bets are incorrect becuase the equity advantage is too little compared to positional disadvantage (obviously this is soemthing I should of figured out in ring game play too, but it happened much less). Is there any formula to calculate what range you should 3 bet vs his range of openers?

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equity is only one factor to be considered here. i feel like an idiot posting this over and over, but you have to consider how the hand is going to play out postflop. will your opponent be intimidated by your 3 bet and fold easily/ play passively? will he call down big cards to the river because the pot is big? will your reraise change how he plays a pair on the flop/ turn? if an ace comes will he fold the flop with no pair/ no draw? will it stop him from bluffing later in the hand? how will it affect his semibluffing frequency etc. and you can ask similar questions about how he plays when you dont reraise. a lot of these questions depend heavily on your image and his. then you relate all that back to the type of hand you have, not just your equity.

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2. When you open raise and only get called by the BB, SB, and/or both;

Under what conditions would you check behind on the flop holding overcards that include an ace?
Under what conditions would you bet the flop and check the turn?
Under what conditions would you lead both for the free showdown?

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this is such a complicated question that saying anything about it would almost be pointless. 3rd st almost always bet. 4th st heads up you should be a decent favortite to bet, but not every time. 3 way check more often depending on who/what youre against. dont forget to bluff 5th some % of the time, dont always take the free showdown.

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3. This is a question I feel stupid before even asking. Should you/how often check behind on the turn and/or river against a tight caller who is also super passive and will c/c even with TPGK or 2p?

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its a tough question because him being tight makes you inclined to check, but him being passive makes you inclined to bet. its heavily flop dependant (especially how many draws are out) and also depends on how hell play the river after you check or bet on 4th.