As others have said, I'd avoid both of these cars.
#1, clearly rebadged and modified (likely by a younger driver, which leads me to believe it was more likely abused). Then again, most all of these cars in used condition have likely been driven hard. Good news is, they can handle the abuse if properly maintained. Dealer also seems to not be knowledgeable about the cars, which isn't uncommon for dealerships, and also very willing to mislead the buyer (you).
#2, usually ideal to avoid any cars that have been in a collision, unless you get them inspected by a trusted mechanic. Price is alright, but nothing to jump at.
The "plethora of issues" is a bit of an exaggeration. These cars are quite reliable, and issues tend to be cosmetic in nature (generally only with very early models, and even then not all of them), a completely common effect of modern high flow fuel pumps and nothing to worry about (see: crickets), or some transmission issues (worth reading up on, but not a significant enough issue that I'd advise against buying one).
A bit of my personal experience: I bought a used '13 in the summer of '14. It is red and had 4,100 miles on it at the time. I paid $23.5k OTD from a local Subaru dealer, after talking them down a bit. Mine was built in the 2nd half of the first production year, supposedly after the body fitment issues had been resolved (not all early models were affected by this, just inspect the cars thoroughly with a scrutinizing eye). I also was involved in an accident in my car, in which I hydroplaned in a storm, spun out off the road through a ditch and into some thick brush. The car was mechanically sound, but did around $6,800 in cosmetic damage. Not all accidents mean the car is going to be full of gremlins, but anything with collision noted should be examined by a professional (with a specific focus on damage to the frame of the car).
I say to keep looking for the right deal, there are lots of these cars on the used market and there are some good deals out there, and to do all the research you can in the meantime. Ideally you should know more about the cars in general than the dealer/seller when you go to look. Always have used cars inspected by a 3rd party (non-interested) mechanic that you trust. If you don't have one, ask family/friends if they have a trustworthy mechanic who can do an inspection.
As for the modifications, the exhaust your son seems to be interested in is a fairly cheap one that can be picked up new or used for not that much ($300-500). I wouldn't let that be a deal breaker on the car.
A side note, and I'm not trying to scare you off here, but these are RWD sports cars, and while they may not be fast a driver can potentially get into trouble if they're lacking in skill. (Even skilled drivers crash too). Generally speaking, RWD sports cars aren't the ideal choice for a young person's first car. My first car was an 2000 Toyota Corolla with an automatic transmission. An excellent first car, but the bane of my young speed-hungry existence at the time. lol But we're enthusiasts here, so I won't steer you away from buying your son an FR-S. I welcome young new enthusiasts to the community! I just caution you to fully do your research.
What I will recommend in regard to building driving skill is to look into autocross with your local Sports Car Club of America (SCCA) chapter. You can read up on it here:
https://www.scca.com/pages/i-want-to-autocross But I'll give you a brief rundown of it
Autocross is a fairly low speed/low risk form of motorsport that takes place in some sort of large open lot. Drivers take turns navigating a cone course as quickly as possible, with the goal of getting through the course in the fastest time. The nice thing about it is that the tighter course design means lower speeds/low risk. You're unlikely to exceed 60mph in these cars on most courses, with an average speed closer to around 20-40mph.
A few benefits of autocross:
-It'll teach your son more about car control, and in theory should make him a better driver. They usually hold instructional in the beginning of the year (and experienced member are always willing to lend advice/instruction throughout) It also teaches you to respect the limits of your car, and hopefully provides an outlet, for all that speed lust, that isn't on public roads.
-It's an excellent activity for you and your son to do together (hooray father-son bonding!)
-You can do it in a completely stock car without any real preparation (just make sure your oil and brake fluid are at appropriate levels).
-It's a lot of fun
(Excuse the long reply, I've got 30min of work left and this helped me kill some time haha)