Can I airdrop all contacts at once?

As long as you are using iCloud with contacts turned on then when you sign into iCloud on your device again all your contacts, calendar items, reminders, etc. will be restored. However, if you really want to back them up there is an app called Simpler that will allow you to back up and restore contacts. If I remember right it is free with some premium options for in-app purchases.

No. AirDrop one at a time ... if you choose to use AirDrop.

lillian199 wrote:

I am unable to back up my iPhone for some reason.

I would pursue a solution to that problem first. Are you trying to backup to iCloud or iTunes? What happens when you try?