>1) Is there any way that I can create a new table in VFP6 and add it as a table to that Access database?


Not directly. You can use COM Automation or a program found in the database here at the UT: DBF2MDB


>2) May I add a new field to tables in the Access database while I am in VFP6?

Through COM Automation you can get full control of Access (must be installed in the same machine).

I do not use MS-Access or have it installed here but I don't think you can do it through ODBC.