I just use debian for my ventoy. But all you really need is a proper partition manager.
I’m not sure I know what you mean by diagnosing, but it’s usually a good idea to use the same distro you’re having trouble with.
Depends what you’re after, but I’ve always been partial to gparted live.
Me too but I might replace with https://www.system-rescue.org/System-tools/. Gparted live is really hard to customize and doesn’t run as root, makes no sense for a rescue tool. SystemRescue also seems to come with something similar to rEFInd to boot broken systems…
I’ve gotten good mileage out of just an Ubuntu live image. If the network is working you can install packages via apt like normal, but they include a lot of the basics already.