Company Registered Email Address & API Call

There is no registered email address of a company.
Companies House do not collect or hold that data against a company.

The page limit you have experienced is a limit we have set on the service, more details here:-

Our search functionality is designed for customers who are looking for a specific company, not for paging through multiple pages of ‘close’ matches.
There maybe other products that are more suitable for your ‘matching’ requirements, for example our bulk product at:-
http://download.companieshouse.gov.uk/en_output.html

Hope this helps.