You will be entitled to a State Pension when you are 67...get a State Pension forecast here ::::
https://www.gov.uk/state-pension-statement
This is easy-peasy, and will take about 10 days. The eventual amount you will get in 2030 will be different, as new pension rules could be brought in by future Governments, and/or you could start working again and therefore start paying National Insurance Contributions again.
I am unsure what exactly what will happen to your Civil Service pension, but it should be payable for the rest of your life.
I can't help you regarding the ESA I'm afraid.