Not sure you mentionned it (I probably missed it), but which engine in the Sport ?
Yeah the clock setting : probably a sleeper car lol. Most probable is that battery got badly discharged/died at one point and clock got a reset.
As for tire pressures : as far as I know, the jump to 36 psi in 2015 (for most 17'' tires) happened out of the blue, probably for mpg improvement. You can safely drive yours at 36 all around, if you so chose.
Battery : yep that cover is a PITA. You have 4 options I guess :
1) Remove cover and check (pain...)
2) Use scissors and open up a corner of the top cover, say near the negative post, to see part of the battery. OEM battery is easy to ID (I have pictures of my OEM battery you could look at). Don't do this near Positive post, to avoid possible shorting out with nearby metal). Then use Gorilla tape to re-seal the cover (hoping Gorilla tape sticks to that material... uhm...).
3) Use a battery tester to check status (like the Ancel BA101).
4) Let it live until it dies...