Simple series of questions:
Is it wrong to put your front wheel into the mallet of someone tripoding in goal? It's one thing to take space by putting your wheel between their bike and their mallet so they can't tripod, but I mean intentionally hitting the mallet with your wheel. Like a wheel shot, but you want to hit their mallet out of their hand or off the ground.
Is it wrong to put your front wheel into the malelt of someone dribbling? Imagine that I'm shuffling the ball up court, it's right on my mallet head and a defender puts his wheel into my mallet, making me lose the ball. More importantly, if I'm dribbling the ball and a defender puts his wheel over my mallet head and foots down, I'm obviously shouldn't have to tap because I didn't initiate the contact. Yeah, it's wrong to attempt to get the ball and put your mallet under someone's wheel, but if you already have the ball, you shouldn't be penalized for their wheel going over your mallet.
none of the scenarios you described sound illegal to me. you can ride your bike wherever you want as long as you're not t boning someone, and that includes between their mallet and the ball/ground. personally i find that my mallet is much more effective for stealing the ball and footing goalies, but to each their own i guess.
if someone runs over your mallet and you foot down then you gotta tap out, doesn't matter who initiated what.
i can imagine scenarios where wheel/mallet interaction could be considered unsafe or bullshit play. i'd have said that it would fall under the "don't be a dick" rule, but apparently we're not playing by that one anymore because it's unfair to all the dicks.