Your strut sounds knackered to my. There shouldn't much free play and the piston should rise when it's been pushed in.@Alibro - When you removed your strut could you see anything wrong with it?
Reason I ask is that mine all looks fine and the only thing I notice is that if I retract the piston the whole way and then press the piston in, the first 10mm of travel happens with no resistance and then I feel / hear the fluid causing resistance.
I think I read on here somewhere that is not correct.