As a retailer, I would expect that at the time the estimate was put together, the person had to know that the carpet was a stripe, and planned the amount of carpet required accordingly. If the job was always for a stripe on the stairs, it's the shops responsibility to quote and order correctly.
If the shop knew it was a stripe, quoted for a stripe, supplied the carpet, and did'nt allow enough carpet (planned it for a plain carpet) then they have to resolve the issue at their expense, OR come to an amicable agreement with yourself if you are happy to contribute towards their mistake, how far you push this point is up to you.
With regards the extra carpet, they may have discounted the carpet to the point that they have charged you just for the amount required to complete the job, and will probably be hoping that they can recoup some of the 'loss' by selling the waste as a remnant, it is likely that as you only needed a small piece to finish, then quite alot of carpet needed to be ordered, so if they charged you for the small piece,I would say they are entitled to keep the rest that you have not paid for and try and recoup some loss/break even.
Regarding the door bar, that's just sloppy, but they did'nt break the tile, unfortunately you did (unknowingly admittedly) but ultimately they are not directly responsible for the damage to the tile, they should be cutting the bar to the right size and re-fitting though.
