Can I access sdf (SQL Server Compact database file) kept at some other computer on the same network?
Try Replicating Data to a remote server. http://msdn.microsoft.com/en-us/library/ms152568(v=sql.105).aspx
SQL Server Compact is just not designed to be used in a network. It's designed as a local-only cache/database store. It was a design decision made by its authors ... if you need something that works for multiple users in a network - use the real SQL Server (Express or any other edition) (by marc_s
It is also considered bad idea to expose SQL server to network - you may want to redesign your application to have service exposing limited functionality to users and calling DB (in this case you can use local SQL compact, but still consider other editions that are more appropriate to general data storage).
If SQL Compact is requirement - replicate data to local file - MSDN:Replicating Data to SQL Server Compact.
For more information on Sql Compact connection strings - Connecting C# to SQL Server Compact database