(1.1) Yeah I think you're still not quite understanding what improvised attacks are for (which is perfectly reasonable because they need a more thorough explanation as it's a wide umbrella). On the one hand it can be as simple as "My MEC lost all its attack parts, I slam into the enemy with DUR" at which point I might rule Hit = 1 DMG. It also might be something like a player saying "I shoot down some stalactites to slow down my enemy" for which I might rule that the player needs to get 8+ hits on a FIN roll and then they can cause Stuck and deal 3 Direct Damage.
The key words here are "I might rule" though - Improvised actions is where the system goes pretty hands off and asks for GM fiat to step in (After all, if it wasn't the sort of game that needed a GM it would just be a video game). Improvised Actions (and Attacks) is an explicit rule to say "You can use your actions for things that don't have an explicit rule."
(1.2) Yeeeeah I really should nix the MOB scaling... I'm not sure what you mean by Stat contributions can be the effect of specific Parts, Stratagems, or Perks - Since there are Perks and Parts that explicitly boost your Stats though? (Be it Shields, Armor, any of the core ones etc)
(2) Hull could work too (And I definitely prefer it to Armor, and it's vague enough to feel appropriate)
(3) I understand your argument, and were the goal of this game to have each part be more similar in utility then I might consider it, but you mostly lost me when you argue there's a bad kind of variety (To me the only bad variety is if a Part was like "Hey here's 10 billion DMG for free" not "Hey this part is hella niche" especially given there's nearly 200 of 'em having some mechanical outliers is good). The Chances aren't changing any time soon and I really don't think they need a separate keyword when their mechanics (a certain condition must be fulfilled for this side of the card to proc) all work the same. You're definitely allowed to dislike those parts or think they're too risky (heck I wouldn't feel like I was achieving my goals if people weren't split on how good certain parts were) but changing the keyword feels unnecessary TBH. [[And similarly if you feel "punished" by Third Time's the Charm, I'd advise taking another part - That Chance has a very strong anti-boss utility and the main component doubles as some nice mid-range ad clear - And at 5-2 the part is practically a steal]]
I really like their balance and niche as they stand. They have incredibly valuable effects ((True Charge essentially giving you an extra burst of movement + an extra attack on top of the DMG+move you got last turn from Charged Slash, and Giga Blast having an incredibly generous range)) and frankly, as someone who's played the game on both sides, Charged Slash is in an especially solid place (I used the crap out of it and has honestly been worried that it's too strong - especially with how fiercely it combos with Topple [especially if you have both charges up and Unrelenting, it's all but guaranteed] - Which trust me if you build into either of these abilities even as a single MEC you have more control than you may think - even if you have to work harder for it [[which is why they have a higher payoff]). Their Set-up to Pay-off ratio feels solid (if not comparatively generous) and if you're the kind of player who doesn't feel like it's worth it, that should be your signal to build into something else ((much like how I have players who try not to take abilities that operate off of doubles/triples instead of the ramps that scale off of dice)).
Inevitably there's going to be parts and mechanics that people want to see seasoned to their own personal taste and it's a reason I encourage GMs to make the MEC Shop their own if they feel there's something lacking, but when it comes to Chances I feel like those are in an especially good spot for how I run things at my table and the experience I was looking to craft. As always folks are welcome to mod the game to feel more "balanced" or however they want it, but for me the game feel is what's most important and all the Chances you mentioned feel like they're capturing their respective kinetics perfectly.
As an aside, I will warn you that if you're going into this looking for a balanced war-gamey strategic experience as opposed to grid-based turn-based stylish action house rules you're going to be sorely disappointed by what's on offer here. The game is unique, asymmetrical, and (especially when you start getting into all the wild stack order stuff you can do) pretty variable in the ways it lets you build and play. There's some parts that I've had some play-testers insist are actively useless and some (including ones you're suggesting are too unreliable) that I've been told are way too powerful and too reliable to be left in the game without nerfing them. Presently (minus some potential minion tweaking) I really think the parts/stratagems available are right where I want them to be, which definitely won't be for everyone, but for the people who it is for they'll feel just right.