1. I want to rename Account Detail to Vendor Detail and not change the tab label.

This can be done by this:

2. Also, there is auto number field on account, I want to rename it. And I cannot seem to find this field to rename in Rename tabs and label setup menu. Please suggest.

If you are referring AccountNumber though it is text field, or any other Standard fields then that label can also be changed upon going through the next screen.

1. I want to rename Account Detail to Vendor Detail and not change the tab label.

This can be done by this:

2. Also, there is auto number field on account, I want to rename it. And I cannot seem to find this field to rename in Rename tabs and label setup menu. Please suggest.

If you are referring AccountNumber though it is text field, or any other Standard fields then that label can also be changed upon going through the next screen.

For custom field label change, you have to use translation workbench.