well whoever you bought the car from was somewhere between a super-tight arse and mad. I guess I can live with different tyres front and rear, but different side to side is downright dangerous in my book....you need consistent grip across the axle. and the thing is 3 of the tyres are terrible (nexen, ziex) and the 4th is not too bad.
if you want your car to handle well it is worth replacing at least the front 2 tyres. Not sure where you are based as you didn't fill in the profile, but you should be able to get ok to decent tyres at 200-250 a tyre.
no point buying one of the best balanced, affordable sports cars around and then trying to drive on shit like that. You might as well have bought a camry.
as for tyre pressures, 50 would be a max level, not recommended. I would normally suggest 32-38 (cold) pressure front and rear - lower for comfort and higher for handling. And keep them within 1-2psi front to rear as well so the handling is consistent