Translation:She is Mr. John's grandmother.
I quite agree, honorifics would not be used with a given name. While I found there was Mr. or Ms. John as a surname.
It would be recommended to us a name which is exclusively used as a surname, e.g. Smith, Brown, Robertson etc., to avoid misunderstanding of learners.
Yes, you can use 彼女 in this case, thus 彼女はジョンさんのおばあさんです is equally correct. この女の人 is neither respectful nor derogatory, just neutral. This may be literally translated as ”this woman/lady".
If you want to say it more respectfully, use こちらの女の方 or こちらの女性の方. Generally 方 (kata) is an honorific expression of 人.