The hairs coming through to the underside of the base are normal. That happens over time, and you just have to cut them off. It happens more quickly if you rinse the piece with water pouring from the hair side to the base side.

Are you saying that the poly (plastic) rim has become deformed and crinkled up? That would seem to suggest it was affected either by heat or by chemicals - I can't see how it can have been caused by conditioner. The only thing I can suggest is that you try to straighten it out by playing a warm hairdryer on the poly and rolling/stretching it flat. If that doesn't work maybe you could peel the poly rim off and use just the lace? Is the piece wearable as it is, or have you got a spare?

To be honest, this doesn't look like a hairpiece of the quality you would get from Toplace, and even if you can salvage it I am not sure it is going to be wearable much longer. My feeling is you should be ordering a stockie pretty quickly so that you don't get left exposed without a wearable unit. Where are you based?