While walking through the forest, on the way to confess to your crush, you come upon an old house. Outside of this house is an old, damaged Brazen Head, with a hastily wired coin-slot appended beside it. You'd like to know how your crush feels before asking them, so you take out your coin-purse
But, before you can sacrifice your hard-earned pocket change to the Head, you notice a rather spirited discussion scrawled on the wall of the house. Reading this, you learn:
Due to damage, the Head needs about a pint of its nectar to answer one question, which is unfortunate as the leaky tank holds only 3 pints in total. Overfilling the tank will make it spill out and damage the machine (and your shoes)
The corroded pipes and poorly-made pump cause the Head to act differently with different fuel levels
When filled to 3 pints it manages to give a truthful answer to yes-no questions, otherwise keeping silent
When it's down to 2 pints it will only lie and try to answer unanswerable questions
When on its last pint it'll give out random answers
Once it's empty it won't say anything at all
The Head is much quicker when a question is repeated than when a new question is loaded in
The tins piled beside the Head are pint-sized and contain nectar to fuel the Head. They are also free to use, but rather short in supply
The Head shouldn't be refilled while it's working, but between questions it's perfectly safe
You can't tell how much fuel it already has, and you don't want to waste money on unnecessary questions. How many questions must you ask (in the worst case) in order to fill up the Brazen Head to 3 pints without overfilling it? A bonus if you can also use the least fuel and ask the fewest distinct questions