Mazros

It seems movement with the arrow keys is based on where the camera is facing, if you move the camera so that it is in line with the grid as opposed to on a 45 degree angle you will be able to move the 4 directions. That worked for me, atleast.

I experienced something similar. The end turn button was grayed out as I was trying to press it. It turned out that I had an auto battle still going on somewhere and I had to move the screen to it and let it complete before I could end turn. For some reason the auto battles can sometimes take a long time to complete so I do other things while I wait for them to finish.