I also can't see the photos but it's pretty straight forward, if the OP has read the tires and they do indeed say 35lbs max on the sidewall, I'll take their word for it, I mean tires of many years ago use to max out at 35lbs and possibly cheap Chinese tires still do(OP, what brand are they?) that said since they probably are "cheap" tires it would be one more reason to not over inflate them. Sure they haven't blown yet, but do you want it to happen when going 70mph down a busy freeway
no I'd immediately lower the pressure to no more than max inflation pressure when cold. Don't worry about what they get to warm, max inflation pressure is always cold and they assume the tires will get to a higher pressure when warm, that part is built in the spec. What you don't want is to over inflate the tires when cold, then they'll get even more over inflated when hot.
I believe exactly what someone else said, the car was a lease return and either the previous owner got the cheapest POS they could to pass the inspection or possibly the seller did the same, to be able to advertise "new" or slightly new tires, but I'd more suspect my first scenario.
Leftie biker made a valid point too, it's just how safe you feel with possible sub standard tires, I mean a set of 4 new "good" tires is probably going to cost you close to $500 mounted and balanced, thats your call.....