PostgreSQL requirements for multi workstations Can PostgreSQL run on network environment?  Does it required a dedicate machine to host the PostgreSQL engine, like MS SQL?

What am I trying to do is having multiple workstations can access to the network database at the same time, without connect to dedicated host machine.  The MS SQL Express doesn't allow me to put the database to network drive.
Yes, PostgreSQL is fully network aware. You can put it on a separate machine or not, this all depends on how you use it, so you will need to state your requirements, type and volume of data, etc.

See for example https://www.postgresql.org/docs/current/static/runtime-config-connection.html and https://www.postgresql.org/docs/current/static/ssl-tcp.html

For development purposes, you can install it on your own machine to develop your programs and later just move your application to use the production database.