Check vacuum hose behind the intake manifold. If that slides out a bit, it will be very rough. If not, change your intake gasket. A $5 part that makes a bid difference.
You drove 40k and it's still red? I believe you're in luck. Drain and refill is fine. I am actually draining and refilling 3 times on my corolla and accord just because the fluid was black. Once you do the 3 drain 3 fills, you need to just drain and refill once every 30k miles. Since yours is...
That engine is so small that you can dance around it :P
This is the best video I found. I haven't done it on a corolla yet, so I can't tell you exactly how to do it. I'm sure you're a bright man and will get it done. :thumbsup: If you're skeptical and don't wanna mess with it, just call some...
Is it cold where you live? Did it just start when the cold came in? I bet you it's probably the power steering pump. Needs replacement. Is the wheel hard to turn? Had the same thing on another car of mine.
Did you ever take off the transmission by any chance? Check the bolts holding it in place. Could be a loose bolt, but it could also be something in the transmission. My wife's tranny went bad at 60K, but that's probably because her brothers did stupid stuff with it.