Yes, you provided what was requested.
Yes, you have a problem.
>I get this error
>TNS:listener does not currently know of service requested in connect descriptor
>when try to connect from C# and Oracle.DataAccess to database.
>When using sqlplus from that machine i can log in to database on other machine with same username/password.
The fact that the connection succeeds when using sqlplus, means the DB server is properly configured.
Therefore I conclude that the problem only involves connect from C# and Oracle.DataAccess to database.
I don't have incite into how to debug C#.
As a possible long shot in solving this mystery please try the following & post results.
within the connection string change "XE" to "xe".