Can I play Single Strike Mustard if my Bench is full?
No, you cannot play the card. Since the Bench is full you cannot search your deck, and since you did not search your deck you do not get to draw 5 cards.
Source: TPCi Rules Team (2022-09-08)
If I use Single Strike Style Mustard to put Duraludon VMAX directly onto my bench, can I later use Cheryl to remove damage counters from it despite it not having evolved into the VMAX?
Yes, it is still an "Evolution Pokemon" since it has an Evolution box printed on it. It would not be an "Evolved Pokemon" but that is not what Cheryl requires.
Source: TPCi Rules Team (2022-06-02)