I have had an @me account for years and now suddenly I am receiving emails addressed for @icloud and they are for somebody else. How do I stop receiving their personal emails and know that mine are also safe and only being received by me?
It looks like you Apple ID has been compromised. If you think you have evidence that your Apple ID has been compromised https://support.apple.com/en-us/HT204145
If you want to change your Apple ID or your Apple ID password see
Change your Apple ID (Be very aware of the restrictions here.)
https://support.apple.com/en-us/HT202667
Change your Apple ID password
https://support.apple.com/en-us/HT201355
What to do [before or] after you change your Apple ID or password
receiving someone else' emails
