These are common problems on these cars, don't worry! no need for the extended warrantee.
The 3rd gear problem can be resolved by switching to some other tranny fluid, or by warming up the car then opening the fill hole on the tranny. There should be some excess fluid that will leak out, and resolve the problem.
The surging is simply an inconvenience; I've had mine for over a year now and I've gotten used to it.
Every si owner ive talked to has noticed these little bugs. It's nothing to worry about. There are pages and pages of this sort of talk on the web, search google for more info.
oh, and welcome to HAN