Ok so here's the problem. My car starts fine and idles fine however, when I rev the engine, it revs fine but when the needle is coming down it goes below 800 to 400 or 500 and comes very close to stalling. It manages to catch itself then resume running normally. I'm not sure if it may be a vacuum leak because there aren't any visible signs that there's a leak. A many inputs as possible will be greatly appreciated. Thanks.

 

Sounds like you might just need to do an idle air relearn. Just check the air filter first. You can also clean the mass airflow sensor and throttle bodies but read here before you do that as people have caused damage to there Zs cleaning them wrong.