Do I have to sign this form and does it have any legal validity?
No to both parts of your question. There are only two forms you need to complete for your renewal application.
The first is the official buff coloured application form (form 103) which the police should send you or which you may have to download from their website and complete.
(The form on the Essex website is interesting in that it is the copyright of the Sussex Police and I wonder if Essex have formally sought approval for its use.)
The second form is issued by your bank and commonly known as a cheque.
No other forms have any legal validity whatsoever in the renewal process but they can be quite useful in an emergency if you run out of toilet paper.
The unofficial Essex form is particularly bad because it implies that your certificate may not be renewed in time and in that case you will be allowed to keep your guns without a valid certificate.
No matter what the police may tell you it is UNLAWFUL to be in possession of a gun without either a valid certificate or a Section 7 temporary permit.
There is no way in which the police can authorise possession by requiring you to fill in a form or in the text of a letter.
You should write to Chief Constable Jim Barker-McArdle personally and complain about the sloppy performance of his licensing staff and the fact they are encouraging unlawful possession of shotguns.
I spoke to the newly appointed Inspector who deals with these things in Chelmsford and he seemed quite surprised at the reaction the form had attracted.
Maybe he needs to learn more about firearms law before trying to run the licensing department.