can mysql work like ms access?
ms access save a file as mdb file and can bring to any where, when run the application, data can be straight away updated into db file, no need rely on the server.
so can mysql do the same thing?

The short answer to both is no, as MySQL is a client/server based application:
...where as MS Access keeps virtually everything contained in one file.

This is not entirely true, for wherever the .mdb file is taken, the MS Access application must be available to use the DB. Won't be very useful taking the .mdb to someone using LINUX/UNIX, for example.

However, MS Access can be used as a front end to MySQL if there is server availability, and there is also ODBC things that can be done too. See this page for topics about MS Access and MySQL.