@Kudee, If you have downloaded offline maps you should be able to navigate without internet connection. Just when calculating the route it needs internet connection. Of you enable off-line mode AND have maps downloaded AND you download the route in advance, THEN you can start the route completely internet independent. There is work being done to smooth that experience.
About the Compass, you should not need to tap it regularly. I am afraid you are touching the screen or moving the map slightly by hand. After that you need to re-center the map to your current position (which is done by tapping the compass). The MRA team is working on automating the re-center when movement is detected.