The Pre-cat was fitted some z22se for emissions but was not a requirment in the UK so is not needed, it app holds back about 5bhp and can cause cracks in the manifold. If your car has one fitted it is a DIY job to remove it. There is a how 2 do it in the how 2 section. newer manifolds dont even have them now.
The exhaust "cat back" is what it says really a centre section and backbox. Cost can really vary. If cost is a issue and you have a irmsher back box or similar then the centre section alone will help and costs are about £65 + fitting. Other then that you can have a full custom sytem built for about £360 +.
I would start buy cleaning your throttle body an easy DIY job to do with some carb cleaner.
Then i would have a look at the EGR valve, if this turns out to be faulty donate to the site and you can get a cheater that our tech mod has created to save you £££ on a new one.