They are covering themselves - nothing wrong with that. They feel because of your past they don't want to risk sending you the item without full payment and they are within their rights to do that.
Although in this case it appears to be have been a mistake any company can stop you from buying something from them if they feel that it's not worth their while dealing with you. I assume usually Gems TV would contact the person first though rather than just cancelling the account and it looks...
No, you are allowed to open it and have a look at it properly to make sure it's suitable for what you want.
The idea of the DSR rules is to allow you to have a proper look at an item the same as you could do in a shop.
No, just let customer services sort it out. The op has only contacted them once after sending the claim form in. They have to let customer services sort it out first.
Not how it works - if an advert is wrong then it was a mistake and they will refund you but you can't expect them to send what you weren't meant to get in the first place.
If they advertised 6 and you got two then you can send it back for a full refund. They must also refund your initial postage cost and the cost of the return.
Which I don't think is a good thing as it means we don't have 'free speach'. We can say what we like as long as it conforms to the rules is not really the same thing.