Oops sorry for the late reply sammifan! Yeah man it's surprising haha I'm always cruising somewhere
Do you attend any meets yourself? I mean I go to JDM monday once in a while, I've yet to go to a Mazda meet at marché centrale and I've been to a few vaudreuil meets this year but yeah man hopefully we cross paths one of these days. Doesn't even have to be at a WI meet (truth be told I've only been to one)
Check compression, turbo seals, see if rear diff is leaking, a/c compressor, make sure PCV isn't f***ked, use a magnet to go over the body below the door handles(used to be a problem where you could kick the door lock hard enough, it would open) and make sure it's been running proper oil. The engine can start running into problems after you change the timing belt usually because people cheap out and only want to do the water pump/belt whereas you should be checking the overall health and internals of the engine. Additionally the car doesn't handle improperly done mods. It's silly to say but there is an order to modify the engines, it handles boost and mods reliably upto a certain point but if you don't do things in order then certain components start to wear quicker and then you run into bigger problems. Exhaust, intake + accessport and you're up and running at a reliable tune with loads of power and sound
I've learned this through the problems Mazderp has encountered and from general tech that I know about the 2.3 DISI that the speed3 and speed6 use!
87 would certainly harm the engine yes. The grade of octane is the temperature at which it ignites. Lower numbers mean it ignites at a cooler temperature where a big number needs more heat so it would screw up the engines timing because there would be delays in ignition. Over time I'm sure this could harm to the engine but don't quote me.
If you're buying your parents speed6 then there shouldn't be too many issues as at least they've driven it better than most and assuming they brought it to the dealer for all maintenance!
Good luck on your purchase