For #1, the Scosche app does upload fit days files I think but otherwise pretty limited. Probably you found this already.
For #2, apparently there is a de facto standard for sending hrv data from a hrm, and Garmin does not read it at least on my FR645M. I spent a while working this out and ended up turning off that feature on the watch and instead use hrv4training. I've been generally positive about my first Garmin watch, but this aspect has been a total fail as it has pushed me and my money outside of their ecosystem.
I do really recommend hrv4training - the developer is a scientist and packs a lot of info into insights once you've logged month+ of data and he rates the r24 highly, but it likes/ needs Strava / training peaks / whatever for workout info.
For #3 clearly the hrv mode sends the additional time between beats info and probably does less/no smoothing of beat data. For running it would smooth the beat data and might turn on the cadence sensor, though I've think I seen that when left on hrv mode when I start an activity. My watch switches the r24 to running mode automatically when I start the running activity, so remember that for your testing and I manually switch it back to hrv mode after winning. I haven't investigated the other modes.
I'm replying to all of these old threads because I think I found a workaround to overlay HR data from Rhythm24 onto a Garmin .fit file. There may be other ways to do it, but the one I'm using is with an app called "Fit File Repair Tool", at the link below. It's really pretty simple. Note that it is $50 for a license, but I've used it for a lot of different data editing things, so it's been worth the investment for me.
You first import the primary activity file, then import the Rhythm24 file using the "Merge Mode". After a couple quick box checks, export as a .fit file and import into Garmin Connect (or whatever other data manager you choose).