The automatic shifter cable in my Rio wore out a while back and got really hard to shift, I was going to suggest that maybe the same was happening to your clutch cable, but sounds like maybe not if spraying into the clutch components fixed it for you.
Is it the original clutch? It's probably close to time for a new one anyway if it is, good time to clean all the other components.
I second the IAC valve being your bad idle culprit, you can try cleaning it with carb cleaner, but in my experience it'll be back doing the same thing very soon, I replaced mine and it's been fine since.
My cars: 2003 Kia Rio, 1977 Dodge W300 Wrecker, 1986 Chevy Monte Carlo, 1977 Ford F250 Wrecker, 1985 Subaru GL, 1986 Audi 5000S, 1990 E150, 1983 Chevy Monte Carlo, 1982 Ford Mustang, 1978 Ford F150, 1988 Mercury Grand Marquis