My Xbox 360 has an E74 error and single red light. Is there any way to fix that without having to send it in on a repair? How long do the repairs take?

If e74 is caused by the same thing as the three red rings, you can order some washers off ebay and try fixing it yourself.

It is the same fix, but I would recommend sending your xbox in if it is still covered by warranty. There should be no cost to you, and you get a completely refurbished system instead of your repaired unit. My experience with the red ring repair under warranty was approximately 2 weeks without an xbox. Any normal adjusted human being should be able to survive that long.

I'm almost sure it's still under warranty. Is the warranty extended when I get it back?

Yes, I just had the same problem as you. Microsoft fixed it for free, even though it was out of warranty, and gave me a warranty for a year after the date I got it back.