I've done it before on a really old Kindle... KOReader isn't precisely an alternate firmware. It's just a piece of software you run on the Kindle in place of the default, and it does have its advantages, at least on my old Kindle: for example, I could enable Night Mode and read ePubs. It also supported connecting to Calibre wirelessly which was also convenient-ish (Calibre still eats up MIME types and I was very happy on the day I could finally uninstall it, and KOReader doesn't support using USB to transfer without first stopping KOReader). Other than that, maybe it's because my Kindle was aging, but the battery life seemed to worsen dramatically after jailbreaking, and I had to downgrade to an older firwmare in order to jailbreak it.

The Kindle was getting old and I bought a Kobo anyway (in part because I'm tired of contributing to Amazon's empire, and further propelled by the fact that it supports Adobe DRM'ed ePubs [and well, while I don't like DRM, it's nice to be able to have the option of using my local library's ebooks]). I'd think you're correct about the Kobo's jailbreaking (haven't tried it myself, but I do intend on doing it in the future, and perhaps developing software for it), but I know already it's much, much easier to customize, thanks to the wonderful hidden folder with the Kobo eReader.conf file, where you can, for example, set the power button to screenshot (which disables the power button, but I have an aftermarket magnetic sleep cover, so this isn't an issue).

Have you tried doing a hard restart? Sometimes my kindle gets stuck and needs a reboot, especially if it has been left alone for a while.

Odd. I've never had this issue -- plug it in and the mass storage shows up. My platform is Linux, but this shouldn't make a difference.

What I have seen, however, are plenty of micro USB cables which do not have the data lines connected. They are intended to be used for charging only and have +5V and Ground wires only.