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This is very hard to quantify without attaching a debugger. I'm inclined to believe you that the effects of stats potentially modify outcomes, but it's also possible there's other side effects going on that aren't explained or are just flat out bugs. 

I personally have noticed the 101 flux increase, but this was without charm magic as well so I really can't say whats up there. More testing is required

I did a test where I found the save file and manipulated it to only have 10 levels of speedup. Ran two instances of the game, reset the save on one, and checked if there was a speed difference. There is. It's insanely subtle. I recorded a gif here https://i.imgur.com/xJPyY25.g

It's not on repeat action so they're not accumulating stats either.

It's much more noticeable with 300 levels :3 https://i.imgur.com/pSSdA5W.gif

again, it's insanely subtle. I'm pretty confident that it's the speed up buff, but I could concede that it's too many variables to measure because I have more than just the speedup buff between the saves. 

Action time is steady between the first and last action, and xLv is only the ease in which you gain the level. As it's the first action in the list it's starting from baseline stats. Without slowing the game down I can't accurately time how long it takes in seconds for X flux to drain, but each action takes exactly 100 flux regardless of level. Modified amounts of flux are reflected accurately in the cost as seen with travel costs and the "Pack Mule" skill. the action is faster, therefore the drain is faster. 

Speed up does work. It's incredibly subtle though. I have two saves, one with 3 speed up, and one with 13 speed up. the 13SU can do 3 "chat up" operations in the time that the 3SU does 2. so roughly a 1/3 speed increase over 10 levels, which is not a noticeable amount.

I am absolutely in love with this game. I adore the time loop that feels incredibly inspired by one of my favorite idle games Loop Odyssey (renamed to Stuck in Time). Even if this game didn't have any lewd elements I'd be playing it just because I adore the mechanics so much. 
I see that basically every mechanical bug that I've noticed was posted in a major thread with the exception of,

Charm Magic: "Increase flux gain. More flux per flux!"
Appears to do nothing, did a fresh run where I only leveled it and talked to locals and before level 2 and after level 2 the number of flux I had at max was the exact same.

Very fun, I wish I had a cheatsheet to go off of so I could see the rest of the combinations. I have a ton of unused slots and feel like I've tried every combination available to me.