2009 Corolla 175K miles - Couple of issues, any suggestions?

I always thought I could reach 200K miles but my car is having a couple of issues, would appreciate anyone's thoughts on what to check.

1. Since about 1 month ago my car occasionally stalls out as soon as I start it. The check engine light came on from this. But I can easily re-start it immediately.
2. It mildly seems to shake or be shaky when accelerating right around 35 mph then stops as soon as it gets past 40 or so (seemingly "shifting" into 4th gear although I have an automatic)
3. Once I'm on the highway around 55 to 70 mph, I can hear a slight rattling sound the whole time. The car isn't shaky at this point, seems to be running fine other than the rattling.

Now, the only diagnosis I've had is from a mechanic who I've gone to in the past who I trust. He couldn't figure it out. His next step would be to remove the engine to check the head gasket but it would cost me over $1000 and it still might not be the problem.

Do you have any ideas?