Hi Archychu
Just to cover the basics as mentioned in the BSP guide the CapsuleApp.efi and the *.cap file are a matched pair and must be used together. When a new *.cap file is released, you must use the corresponding CapsuleApp.efi to install it.
Also I have found a couple of post related to issues with the UEFI , the behavior of your Galileo is different but I think some recommendations are applicable to this situation:
Re: Unable to open serial console session (cable, host OS issues, double check the UEFI shell)
Re: Restore Galileo grub file (I would check the SD card format and size or corrupted partitions)
Regards,