Why haven't you simply change the arguments with the right pah? Copy/paste installed MAME application to another directory will surely fix your problem but will generate other errors. If the default.cfg file is supposed to be present in the installation directory of MAME, and if you have move this directory to another place, that's normal that MAME is not able to found it anymore and assign correctly your custom buttons. BTW, you can define where is located your cfg directory like this :
-inipath "C:\Program Files\mame" -cfg_directory "C:\Program Files\mame\cfg" "%rom%"
For your Xbox controller problem, assing the coin and start action to back and start buttons for exemple using MAME general input menu :