We do have some Mac users here, but they don't visit every day. But I wasn't suggesting to post the logs. Just that you could look at them, and maybe get a clue. I can't decipher Windows' logs either. But just finding out which program or which feature was involved. Often I'll see just a word or 2, and it will lead me in the right direction. Or sometimes there's an error code I can look up.
However, you could try a couple of other ways, to get help with Inkscape on a Mac. There's a user mailing list (which is mostly advanced users and developers), who could probably help. Find the link to subscribe here:
https://inkscape.org/en/community/mailing-lists/ And there's also an IRC channel
https://inkscape.org/en/community/discussion/. You might have to try a few times on IRC, until someone who is familiar with Macs is available.
Either way you go, just explain that you're new to Macs, and you're not sure if this is a Mac issue or if Inkscape is involved. I'd probably try IRC first, since you don't have to deal with the mailing list. But the list is there too, if needed.
Regarding uninstalling Inkscape - I'm not sure. I have uninstalled programs before when the shortcut was not removed from the desktop. I don't remember whether it happened with Inkscape or not. I don't think so. But Macs are different, and I don't know. Who knows, maybe that's the key? It won't hurt to delete the icon, because it's just a shortcut, and when you reinstall, the shortcut will be added again.
For the very last question, about closing or minimizing. Is that only Inkscape where that's happening? Do any other programs which use XQuartz behave like that?