DaemonUmbra

You put them in the server's mods folder

What Driver? Forge is not a driver. Your computer will say that about any program that hasn't paid to be on some whitelist or another. As long as you only download Forge from https://files.minecraftforge.net and only get mods from https://minecraft.curseforge.net you should be fine.

1.7.10 is no longer supported on this forum due to its age. Please update to a modern version of Minecraft to receive support.

The filenames of some of your mods suggests you are not getting them from official sources, please read my signature for more info on why this is a bad thing.

Because they are client-only mods, they don't affect the world in any way

That sounds like you have the mods installed client-side but not server-side.

Not according to the log you provided.

Something's not matching up.

Did you install the mods on the server?

What launcher are you using? Please provide a screenshot.

You need to make sure to run that command in the same directory as the Forge installer, either use the cd (Change Directory) command or in explorer make sure nothing is selected, then shift right click anywhere in the same directory as the installer (making sure you aren't selecting anything as you do so) and click "Open Command Prompt Here", if you see open Powershell Window here that's fine the command will still work.

Ok, try this command in a command prompt java -jar [name forge installer jar including the .jar bit] > installer_log.log.

Please read the "Logs" section of my signature below and provide the appropriate log in the appropriate manner.

1.7.10 is no longer supported on this forum due to its age. Please update to a modern version of Minecraft to receive support.

Where in the launcher are you looking? In the Versions list of a profile or are you looking in the list of Profiles on the start button?

Please read the "Logs" section of my signature below and provide the appropriate log in the appropriate manner.

Is your downloads folder in a OneDrive folder?

Please don't necro old threads.

Where is the installer when you are running it?

Please provide your installer log.

Hmm, when you ran the Forge instaler was the Minecraft launcher running and if so have you restarted it since then?

You can have more than one version installed, I would assume you are confusing launcher profiles with versions. The forge installer will only make one profile, after that it just installs itself as an available Minecraft version for a profile to use.

Please provide a screenshot showing your versions list. Edit: Please provide your launcher log as well

That's your launcher log and it seems to indicate you have Forge installed, an old version of Forge for 1.12 but Forge nonetheless