Ok, so … unlike Windows el al, Linux’s graphic systems are fairly decoupled, so there are a number of moving parts which all work together.
- login screen / greeter, so the Gnome login or KDE login etc
- optional WM or DE selector, typically these are relatively invisible, but names that might come up are things like “sway” or “iceWM”
- optional session type selector, which governs your actual login session and whether it’s running Gnome, KDE, XFCE etc …
For the most part different environments can all co-exist on your machine at once, however the easy way to control your login mechanism is to just have the one you want installed. So the three main ones you might be interested in are;
- gdm (Gnome)
- ssdm (KDE)
- light-dm (others, light-weight, XFCE?)
So apt install one of these should give you the option of making it the default next time you reboot.
Moving on, don’t worry too much about the Window manager, let the session you pick control that for you.
In terms of your session, this is the bit that usually catches people out. You can for example install “gdm” as your login manager, then fire up a KDE desktop by selecting a “KDE” session. There is generally a session selector hidden somewhere on the login page that means you can select your desktop when you log in, and indeed switch between Gnome and KDE on alternate logins, if this is really what you want to do 
The Downside …
So there’s always pro’s and con’s …
… as you have discovered, when you install a different desktop environment, by default it also installs all the tools and preferred applications that go along with that environment.
Whereas some parts of some menu systems are static, some will pick up all available applications, so you can end up with two or three (or more) options for system settings (just for example) all installed and available at the same time. So running system settings from the gnome menus could activate either Gnome or KDE settings if you have both installed.
There’s no easy way around this (at the moment), you actively want installed applications to be made available on the desktop … the future solution will be to install the system side of things as a container (so there is a Gnome container, a KDE container etc), then have a common “/home”, so you can login and get your files, but with the graphical environment coming from a specific contained environment, so different environments don’t bleed into each other.
This is on the way, if you see people talking about ephemeral distributions in the news, this is kind of the direction of travel. Side effect here is that because your installation is fixed / partitioned off, it’s more robust with regards to viruses / malware.
So …
If you choose a re-install, be aware that installing a package that happens to be a preferred application from another environment (say installing a KDE application when you’re running GNome) can via dependencies cause similar issues to the ones you are seeing, in that some KDE ‘components’ can end up being loaded into your environment.
Depending on the scope of the bleed, a better solution could be to just remove the packages you don’t want to see. So if you prefer a particular file manager in a given environment, just remove the others. A simple ‘apt remove’ on the package should also remove it from the menus. (anything that’s auto installed should also auto remove in terms of menus)
You will also find that some desktops are horribly configurable … it’s relatively easy for example to make Gnome look just like a Mac … and KDE very similar to Windows … so if you have something appearing in the top right, it may actually be from your chosen desktop, but a default configuration that’s popped up without you asking. i.e. it may be worth trying to “edit” your desktop settings and see if you can remove it. Gnome and XFCE in particular allow you to add “panels” to any side of the screen, then install menus, launchers, widgets etc into them … which can make them look like “something else”.
(i.e. if it’s “in” a menu, apt remove, it it looks like a menu from another desktop, it’s “probably” part of your desktop configuration that’s been configured by default or by a rouge setting, which you can remove by tweaking your desktop config)
The more you try to correct, the more you learn, the more you can fix if it happens on a smaller scale in the future 