Hi Cris:

Can I get the players' direction in one room?
Also, can I get the scene file's name in one room?

If I try to create a new room to avoid the flash's refresh problem, I found the problem is how can I move the players back to the game in right game scene and direction after seeing the new room.

To have the list of possible directions I think there are some functions to do this, you have to check the developers' reference. You can also check the "text input demo" for some hints.
However please read next:

In general, available ways are displayed automatically according to the links you have set up between rooms.

A good solution would be to establish a mono-directional, dynamic link (NewLink function) from the private playing room (where you would play flash) to the original place you came originally from.

Also placing a "GO BACK" button in the panel would do the same thing and prevent you from having the need to establish links. Just make sure you have recorded in a variable the id of the room where you came from.