AFAIR, you should just need to drag and drop the key onto the mirror (maybe it is the other way around?). Are you doing this with the items in your hero's inventory? Are you sure you have the right key? I did this in the area right beside the cells, but would not expect location to have an effect (except possibly combining them in the BF).
Read the manuscript in the room with the gate and statue, to find out how to open the gate.
<span class='standouttext'>Spoiler : </span><span class='spoiler'>Two red gems did not work, nor did two yellow. Click on the statue and place one red gem and one yellow gem into its inventory.</span> (highlight the text to read)
You do take the dragon gem to the Raanaar ghost.
The BF is separate from the main game. There are no quest items for the main game in the BF, and vise versa. Other than visiting the traders, I have not been doing the BFs at all.