1. you can do them separately. if you can do your disk and shelf firmware upgrades in advance this will make the DOT upgrade quicker - sometimes netapp do not release the latest fw versions separately and can only be applied with an ontap upgrade.
2. the latest firware upgrades shipped with the version of DOT you are upgrading to will get installed if they are newer then the ones currently on the shelves/disks.
regarding the disk qual versions you can copy all versions across:
qual_devices For releases prior to 7.2.1
qual_devices_v2 For releases 7.2.1, 7.2.2 and 7.2.3