Kdenlive is part of KDE, yes.

I don't know what you mean by "story", but KDE is a collection of software more or less (emphasis on the less, at least compared to Gnome) interlinked with each other.

Qt specifically has the LGPL as a non-commercial license for open-source projects. This is part of a deal they made with KDE when it changed hands a while back.

Qt is being actively developed, but I don't believe KDE has any influence on it. They updated the entirety of their stack to Qt6 a year ago, they can definitely incorporate the changes.

KDE and GNOME generally don't care about each other. As for my personal opinion, Gnome's problems have only gotten worse in my experience, but perhaps in ways that don't matter to the average user.

Gnome if you like a MacOS-style UI, KDE Plasma if you prefer the Windows-style.

Generally, any distro will do. Rolling-release ones, or stable ones with a shorter update cycle (like Fedora) will get new features faster, but even Debian has KDE Plasma 6 nowadays.