Can users access database without application on their computer?
Yes, but you'll want to research that approach carefully before deciding to use that option.
If you publish the database to the web (two options are possible, instant web publishing and custom web publishing), then your users can access the database from a web browser. This can be done for internet and intranet users.
Both options add levels of complication to your solution and IWP (instant web publishing) imposes significant limits on scripts and layouts so you would need to research both options carefully before deciding on either of them.
The simplest way to share the database remains opening the database on one machine with FileMaker Pro or FileMaker Server and then other users launch FileMaker on their computer and use Open Remote... to connect to the hosted database.
Retrieving data ...