Linux

Perhaps if you're just trying out and experimenting, you shouldn't use your main system. Try it in a VM, or even better, a spare computer. Then whatever stuff that you like, you trickle down to your main system.

In the case of DEs, I don't like having multiple ones in my system, but only because I like my systen lean. So if I want to try out a DE, I'd just set it up on a test system, usually from scratch.

So far, I'm liking KDE the most, but for something more lightweight, I'd go with XFCE or MATE.

To answer your original question: Theoretically, it could affect your security as each piece of software could have vulnerabilities. In practice, however, it's negligible, and if there's anything major, it would usually get addressed quickly.

Last but not least: When you're just starting out, you wouldn't want to be focusing too much on security. Following the general guidelines should suffice for most case. Just focus first on getting all the functionalities you need. Security usually means restricting access, including to yourself, that means doing it too much could make things not function properly. Securing things prematurely (i.e. before you get things working) could only frustrate you, speaking from experience.

Don't miss the forest for the trees.

Do whatever makes you most comfortable so you don't go back to Windows or MacOS.

As far as I know, none of the major DEs have Windows-style telemetry turned on by default. So ignoring security issues and apps themselves, DEs should roughly be the same on the privacy front.

TLDR; yes it does affect security. But quite likely not by any meaningful amount to be worth worrying about.

Any extra package you install is extra code on your system that has a chance to include vulnerabilities and thus could be an extra attack vector on your system. But the chances that they will affect you are minuscule at best. Unless you have some from of higher threat model then I would not worry about it. There are far more things you would want to tackle first to increase your security that have far larger effects than a second desktop environment being installed.

What do you mean by privacy? If you mean like other people you may live with/come across having access to your data, the best solution is having an encrypted drive/partition. No DE or standard login is going to stop a determined threat actor from just pulling out your storage device and reading off what's on there.

I don't think DE really means much for security, your biggest concern is always going to be the software you run having the same privelages as you (IE filesystem access)

Wayland has security benefits over X11 so choosing one with a Wayland session is a good idea but other than that I'm not really aware of any breakdowns of security between DEs. My gut says the major options are pretty similar on that front, most hardening guides only mention DEs to tell you which ones support Wayland. The choices you can make to harden your system are changing things at a lower level that is entirely unrelated to your DE. That said I'm just a privacy/security interested layperson and security is a topic where you can always split more hairs if you want (or need) to.

That question is very broad.

Yes, double the DEs installed will mean double the possibilities for vulnerabilities.

Also, I know no Linux Desktop that is actually secure. Like having a real password manager or not sharing the clipboard.

Privacy? No? But just look at what data they collecty it is harmless.