Most dentists periodically purge their records of patients who have not attended the surgery for a long time. You will almost certainly need to re-register.
You should probably tell your dentist about your experience with eating disorders as it may impact any treatment you need. Your dentist is a medical professional and will treat this information in absolute confidence. No matter how bad you think it is they will always have seen worse.
How long you have to wait will depend on which surgery you are planning to attend and how many patients they have waiting for NHS appointments. No one can answer that question for you except the surgery you want to register with.
No one on the internet can tell you what any treatment you need will cost either. Your dentist will carry out an assessment and should let you know about any expenses you'll incur before carrying out any procedures. If you are being seen as an NHS patient you will get NHS prices although you might have the opportunity to be seen as a private patient which will come with additional costs but maybe some benefits too.