PostgreSQL requirements for multi workstations
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.