Convention to denote author who left the research group?

From your question, I am concerned that you have not talked to the "author" about the manuscript. You must get permission from all authors prior to submitting a manuscript. It is not acceptable to submit a manuscript without permission from all authors nor is it acceptable to leave an author off just because they have left the group.

As for what is acceptable for an email address and affiliation, almost anything goes (as long as it is not misleading). I personally think universities and research groups should give permanent forwarding addresses to eliminate/reduce these issues.

In terms of the affliation, you should also ask the author. It is not uncommon to list an affiliation as the company/university where the work was done and provide a new corresponding address. As for email, it is common to list only the current address. This might be a new corporate email address, assuming it is appropriate. If not, a personal email or a new personal/professional email address is fine. Again, just ask the author and do what they want.

There's no standard way for this. I don't even assume or care if all the authors of a paper are in the same group at the same institution. Some of my recent publications are half at UT Austin and half at U Buffalo. Getting this person's new email address (even if it's personal) should be fine, though it it is their personal email address, they may want to get a new email address at a new place that they only use for publication affiliations to cut down on the spam to their main personal address.