Patel
a, ESA is a working age benefit and ends when you reach State Retirement Age.
b.You can defer your State Pension as far as I see there is no limit but it can still affect benefits such as Pension Credit and Universal Credit as the DWP may treat you as having a Notional Income.
c. The obvious benefit would be Carers Allowance, subject to your household income and savings then they may be able to claim UC. Try putting your information into one of the online benefit calculators
www.gov.uk/benefits-calculators Gordon