Just a point about missing contributions - voluntary contributions count for pensions but not for contributory benefits such as IB. Only compulsory NI contributions count for those. Yet another absurdity.
As to the other stuff, I leave that to Derek, who fortunately knows more than I do about this.
As far as I know only people who put in a claim for ESA are sent these forms, so it is surprising that you are not entitled to ESA payments at assessment rate.
When you see the CAB and show them all the letters you've received, hopefully they will make sense of why you were sent the forms, and whether you should be entitled to ESA. Please let us know how you get on.