I assume per first example that if I had originally logged him in at 10 watts and later work him on another band and he says 1000 watts, that okay to change?
I can tell you that several times I worked a station twice in ARRL DX and I copied two different powers, and then I did a correction towards what I thought was the more accurate copy, that I corrected the wrong way and lost credit for both QSO's!
Sometimes better to not overthink it. After-the-QSO-corrections can make things worse! Usually better to trust what your ears heard at the time.
Is running a software program that shows obvious typos legal?
I would rather advise that you simply inspect Cabrillo by eye. Especially headers.
Sometimes the things flagged by logging software as "obvious typos" are actually just funky weird-ass-WPX-prefix callsigns. I've logged LM1814 many times in contests, and have it confirmed in LOTW, but every piece of logging software tells me it's an obviously busted callsign :-).
If you go around fixing everything the scrubbing software complains about, you will end up busting a lot of calls that you actually did copy correctly.
If you are a new gun in a contest it can be a little intimidating to ask a running station for a fill. It can be even more intimidating to ask the running station for his callsign! But as you get more experience and especially do contests where exchanges are complex (e.g. NASprint or sweepstakes) you will be more confident about asking for and getting fills.