Yeah, i agree with the plucking. I have grown up with Cockatiels and they have plucked when stressed. Sometimes just moving the cage to a different spot would start it. If it has been back and forth daily it may well be stressed and also if it has been used to the shop owner new parents may freak it out too.
I wouldn't hesitate, take him for a check up by a vet firstly at least for peace of mind. Then if all ok TLC and no major changes in his routine. I think they are generally tough little cookies, we had one that had to have a nebulizer for a respiratory condition. He'd sit on my shoulder and pull my hair!! so cute.
Good luck
