PPups add 1 PP for every 5 original PP. Thus a move with 5 PP will have 8 max with 3 PP ups used/1 PP max, whereas a move with 15 pp will have 24 PP after a PP max.
Pcalc is a thing for 3DS RNG abuse - and 'SoS chanining' yields both a higher shiny rate and better IVs, so its possible its legit. The only way it wouldn't be legal is if it had illegal moves/ability, more than 510 total EVs, and/or the caught level/location was invalid for a wild encounter (hatched from egg requires it to be from the Daycare Couple or a Link Trade. The hatched location can be almost anywhere.). Seeing as its only 2 stats that are good, its likely legal but not the ideal one the OT wanted, so they wonder-traded it. To know for sure, the raw stats arent enough. Nature and level need to be taken into consideration. at level 100, 311 is perfect speed (31 speed IV, 252 speed IVs, and + speed nature). If its legal and optimized for speed and attack, the level 100 stats (assuming Jolly nature) should be:
HP:246-278
Atk:309
Def:145-177
SAtk:130-159
SDef:145-177
Speed:311
if the attack is not that high, another stat (most likely HP) will be likely be higher than what I have listed here.