Hi Finni
Your ESA will cease on the day you reach State Pension age.
Depending on your circumstances you may be eligible to claim Pension Credit which you can apply for prior to reaching State Pension age:
www.gov.uk/pension-credit You are correct, you cannot claim AA as you are in receipt of PIP.
Once you reach state pension age you cannot increase your mobility award. If your are already in receipt of the enhanced component then you will be able to stay on that component, if you are in receipt of the standard component when you are reassessed you will not be able to go on to the enhanced component even if your mobility has deteriorated.
You may want to contact your local Welfare Rights Organisation; You can find your local Welfare Rights Organisation to help you with advice by clicking on the link below and putting in your post code, it will then come up with a MAP with a list of agencies.
advicelocal.uk Gary