Your log keeps saying your system is not allowing access to the game files. I do not know why, the usual culprits are not being "administrator", windows UAC, or your antivírus software. If all this is good, I have no other ideas, and I can only advise you to contact slitherine support.
Regarding your second issue: Steam DLCs are only for Steam AJE. And I think Matrix does not give "Matrix keys" to owners of the steam games, only the other way around.
But there is a non-official workaround: just copy the PAR and HAN scn files from your Steam instalation to the Scens folder of your non-Steam AJE, and you will be able to play all scenarios inside your non-steam AJE.