If you sideload es file explorer, you can update directly from a network share or local folder right on the fire tv. http://www.estrongs.com/?lang=en
I have a network folder just for apk files. If you select the apk file in es file explorer, it will ask you if you want to install/update it. Very handy.
I only use the default Contacts app on my G3, but I know SGIII had same ability.
Contacts App, Manage Contacts, Import.
You could also try an App like ES File manager and open the vcf file. Contacts has an intent for the vcf filetype
Did you try factory resetting the phone or maybe just clearing the app data for Google Play?
You can also use a web browser on the phone and download ES File Explorer from their website, just turn on sideloading. http://www.estrongs.com/?lang=en