Do I need to download the Forge Mod Loader to have a mods folder in my .minecraft folder?
Yes, you'll need to install Forge or Fabric (an option in newer versions of Minecraft) as those are the frameworks for mods which incidentally handles "loading" them.
Minecraft in it's vanilla form doesn't do anything with the mods folder and obviously nothing happens.
If you're struggling to install mods manually, you are better off using user-friendly clients like CurseForge (supercedes FTB), MultiMC or Technic