Bumper reinforcer is just that, to stop the flimsy plastic of the bumper flapping about. It is not part of the MOT, unless perhaps it was missing. Bent is fine.
Can't see why you think the engine has been swapped.
If the dash has a snowflake button, it should have aircon. Press it with the engine running. There should be an aircon pump on the front of the engine (Front being the end with the pulleys, not the side that you look at from the front of the car.) this pump should engage when the snowflake button is pressed and shortly after, cold air should enter the car. You description suggests that the aircon radiator (condenser) is missing, so no fridge gas, no aircon. Probably removed to replace, then not done. (Time, money, availability, etc.)
If that's all that is missing, a new condenser and a regas should sort it.
Other options for a radiator at the front would be oil cooler or turbo intercooler.
Oil cooler would have oil escaping at high pressure, so that's not it.
Intercooler will have large pipes and make a lot of noise if disconnected and significantly less power than you'd expect.
My guess is aircon. Get an aircon specialist to look at it and see if anything else is missing and quote on an evacuate and regas after you've sourced a new condenser.
Bent bumper reinforcer is up to you if you bother to replace. Try this, others may be available.
http://www.clevelandpanels.com/fiat/fiat-grande-punto-06/front-bumper-reinforcer.html
Keep calm. Assess what is needed now, needed later and what is wanted. Then plan accordingly. Aircon open to atmosphere is not good, needs sealing to keep out damp, so this becomes a need soon.
You can't go back to the seller to complain or refund as its a private sale, but you might ask them nicely if they'd tell you what happened and what they've removed/lost. Without any anger, they may be helpful. If they're not helpful, then you can shout at them. It won't fix anything but it may make you feel better.