Do Older Mods Work with Newer Minecraft?

Sadly, no. You're going to have to wait until the creator makes an updated version of the mod for it to work.

Can you use older mods on newer versions of Minecraft?

Older mods are not compatible with newer versions of Forge. They're only able to be ran with the version of the game they were made for. This is because the code the mod uses only fits with the code of that exact Minecraft version.

Can you use outdated mods Minecraft?

It's very possible. If you're using the current launcher, just create a new profile (bottom left) and change the Minecraft version to match what your mod is compatible with. Save the profile, launch it, then quit.