Exhaust will do nothing to harm your engine (unless of course it's blocked...or I guess too small, but as long as you're using parts for an 05-09 GT you're fine). "Cat back" is literally just the stuff beyond the catalytic converters, and at that point the engine/computer does not care. It's merely a matter of sound, metal integrity (i.e. rust problems or damage), and sometimes just age (for the packing, in mufflers that have any).
I would recommend getting some new exhaust hangers and clamps unless they're in great condition. The clamps tend to rust up and they're important to prevent exhaust leaks and noise. The rubber in the hangers dries out or degrades depending on if you live somewhere with salt and such. Have to take them off to do the job anyway so may as well refresh it all. A wire brush and some brillo pads will clean things up, too.
As for the CAI, the answer (IMHO) is generally that it'll be no problem.
There's 2 kinds of CAI kits: those that don't require a tune, and those that do.
CAI's that don't require a tune are basically just for looks. Some people will say otherwise, but if you're not changing the parameters of the airflow significantly (as in, to go outside the stock MAF adjustment range) you're just spending money on a fancy tube and filter. That doesn't mean it's totally bad. There's nothing wrong with a better filter and a cleaner looking engine bay. As for stress on the engine, since you're not doing anything out of the stock conditions, there's no impact.
The other kind of CAI is one that requires (requires as in either "should have" or "must have") a tune. Something like the JLT Series 3 (off the top of my head). Pretty sure the Roush CAI needs a tune, too. Will it run stock? Yes, but you won't get any benefit (will probably be same as stock or even slightly worse). The point of a CAI is to not only bring in colder air (theoretically, though most designs don't do this at all) but to increase airflow for the engine. This in turn changes the airflow that the MAF sensor (Mass AirFlow) sees. The computer uses the MAF reading for the fuel table that the engine runs on, and this needs to be adjusted (with a tune) to compensate for new numbers. The good news is this is a dirt-simple thing to do with your own handheld tuner (JLT usually has a bundle with their CAI and an SCT tuner). CAI canned tunes are commonplace, and for the most part a generic tune will do you just fine. If you want the most you can get, you'll need to get a custom tune, but IMHO unless you're doing other things at the same time it's not that worthwhile.
As for will this (tuned CAI) hurt your high-mileage engine? Most likely not. You're not going to put any high stresses on the engine with just the CAI. I'd even say it's less likely than a no-tune CAI to cause you problems because the MAF will be tuned to where it should be and not pegging all the time.
Hope that helps.