My iMac is slow. Keyboard input very slow.

Determine if the problems also persist in "Safe Mode":



• Safe Mode or "Safe Boot" is a troubleshooting mode that bypasses all third party system extensions and loads only required system components. Read about it: Starting up in Safe Mode
• You must disable FileVault before you can start your Mac in Safe Mode.
• Starting your Mac in Safe Mode will take longer than usual, graphics will not render smoothly, audio is disabled on some Macs, and some programs (iTunes for example) may not work at all.
• Merely starting your Mac in Safe Mode is not intended to resolve the problem, it's to observe its performance without certain additional components.
• To end Safe Mode restart your Mac normally. Shutdown will take longer as well.

You're welcome. Please read to determine if it explains what may have happened to you, and what to do about it: How to install adware

That's a good idea.