The side inserts and front mount can be done without removing the engine. I believe that when doing the side inserts you need to support the motor with a jackstand, but the front can be done without that (though I would do it just to be safe). The rear mount can be done without removing the engine, and if you search around a bit you will find that there are a few recent posts about that. I hear it is much more difficult than the sides and front. I have not done a rear mount, so I can't speak for that.
As far as tearing up your header, it will put more stress on the header and exhaust if you don't replace at least the front and sides, as your stock mounts, if not torn already, will be soon. All that play in the drivetrain may or may not tear up your exhaust or header, but it will put more stress on it, so it's better to play it safe in my opinion. Search around the How-To for some directions and tips on installs, and there are some motor mount threads in the Protege5 forum. Streat Unit (actually spelled with two "e"s) AWR and SLS all make engine mounts, and they all have different durometers (stiffness), but AWR and SU are the only ones that makes a whole set and SLS has had several side mounts fail. StreatUnit's mounts are very soft (60 duro I think) but still stiffer than stock.
Remember that with these stiffer mounts you're going to get more cabin vibration from the engine, especially when the A/C is on. Check out the motor mount threads for more feedback. The general consensus is that adding new mounts feels like bolting on 5-10hp due to the recovery of power normally lost in drivetrain lash. A UDP would be a good addition to the header, and I don't know if your exhaust is a cat or axle back, but protegegarage, SLS and Corksport all make midpipes with a flex section (to take stress off of the exhaust and header when the engine shifts), and you can get them catted or without the cat (my preference, but I don't have to pass emissions either!). I hope all the info helps...happy modding!