This one again. I really wish they’d put up a FAQ for Resolve and its copycat abilities - and everything else that’s needed a FAQ for nigh-on five years now.
The answers to all your questions are yes, yes, and yes. But…somewhere on one of the podcasts from years ago they’ve said that it’s worded poorly and that the intent was to be able to remove a penalty before it gets applied, then Boost Mid - but as you noted, that’s not really how the rules as written work.
If you play it strictly by the actual wording, the main reason to use Resolve would be to remove a persistent penalty (which would still apply to the Boost action part of the ability). It’s also conceivable that you might want to use Resolve when you have no penalties just to get both a Boost and the Min die healing - but you still can’t use the bonus from that Boost on the Min die because you have to declare what bonuses you’re using before rolling dice (barring one reaction that lets you use one afterward, but that’s a real corner case). Still, you might have other bonuses to throw at it, and even Min die healing is fairly rare and could be very useful with the right build (eg one that has reactions triggering from your personal GYRO zone changing).
It’s not an ability that most people get excited about, but even RAW it’s not useless either.
If you accept the podcast statement, a “fixed” wording would be something like:
Resolve (A) You may remove one penalty on yourself before rolling your dice pool for the turn. Then, if you did not remove a penalty, Recover Health equal to your Min die. Finally, Boost yourself.
In all honesty, even that version of it isn’t amazing unless you’re facing a lot of large penalties (-3 or worse), and I suspect it would be best to just adopt a slightly less convoluted and more potent version like:
Resolve (A) You may remove a penalty from yourself before you roll your dice for the turn.
Boost yourself, then Recover Health equal to your Min die.
That makes it a Mid Boost, Min Recovery (which is still only so-so for a Yellow action ability) with a situational rider effect that can quite strong. Automatic penalty removal is the functional equivalent of generating an infinite-value opposing bonus or automatically-successful Overcome, both limited to just penalty removal. That’s no joke, especially when laboring under a -4 persistent and exclusive penalty with no allies available to help get it off you.