While shifting from 1st to 2nd or 2nd to 3rd and having
accelerator open 70 to 80 % the car doesn't seem to
accelerate as it should. Even when cruising around 65mph on
5th and downshifting to 4th (looking for acceleration), the
car will not accelerate right after the gear is in. It will take
several seconds before I start getting anything out of it.
It is pretty much the same for the 3rd gear. Any ideas?

 

Sounds to me like you have a "no brainer" issue here. Your clutch is slipping, which means it's FRIED!! To test if for sure...get the car warmed up by driving around then stop, put the car in gear, put your right foot on the brake and slowly let the clutch out. If your RPM's rise any (even the slightest bit) before the car stalls......slippage!! You can pick up many aftermarket clutch kits for around $250-400 depending on your specific application. Depending whether or not you want a little better than stock, I would reccommend a SPEC Stage II. I got mine for around $320 shipped. Put it in myself in the driveway....so don't freak out if you truely need a clutch thinking that it's going to cost you a grip. It won't. If you end up changing it yourself and have any questions...hit me up. I'll be more than happy to help.

link to SPEC clutches...

www.lmperformance.com