I unfortunately can't help you with the updater issues, but the crash with the BattleForge.exe can be fixed by disabling Direct X 11.
In case you need exact steps:
in the terminal type: winecfg
Under the Applications tab, click the New Application button
Navigate to the Battleforge.exe file and click open
Make sure the Battleforge application is highlighted. You will see the title of the window change to "Wine configuration for Battleforge.exe"
Under the Libraries tab, we will specify an override setting for the DirectX 11 library
In the "New override for library" dropbox, type d3d11 to perform a quick search for the library, then click Add once you found it.
Highlight the d3d11 entry in the listbox, then click on Edit.
Set the load order to Disable
Done