I mean, theoretically? The PS4 can be jail broken, from a quick Google search. And if you can jailbreak a platform you could run whatever code you wanted to. But the PS4 is still vastly more locked down than PC or Android, so it’s a lot harder to cheat (if it’s even actually—rather than theoretically—possible).
Not everyone
I don’t know enough to say “impossible”.
I suspect the answer is something like, “it’s not impossible, but if you do it there’s no way you can ever connect to the internet without getting your account banned”.
My guess is what most cheaters want is the ability to both cheat and play online. That’s the thing consoles seem to have locked down completely. Bans for modifying your software to allow unlicensed code are impossible to appeal, happen with no warning, and wreck the trade value of your now-offline-only console.
So it’s much safer to cheat on PC/Mobile, so long as you don’t mind the devs renaming your account every now and then.
I would not consider it odd. All 5 spent the same amount of gems in the shop, all 5 got x30 per battle, all 5 killed every bird, won every battle. With the new potions, this is easier to do then before.
The amount of birds found is consistent for everyone.