No, this phone will be using GSM technology, which is used by AT&T as well as all other carriers worldwide except for Verizon and Sprint, which both use CDMA. The two technologies are not interchangeable.
not necessarily...
all the carriers use LTE (gsm standard) for the 4th-gen mobile network
Verizon uses bands 4, 13, fire phone supports bands 1, 2, 3,
4, 5, 7, 8, 17, 20.. only band 4 support overlap ("XLTE" branded AWS spectrum....)
you'll get data on LTE, but not voice (until VoLTE is implemented 100% and your phone has VoLTE support... fire phone doesn't look like it has VoLTe support)
theoretically, you could put an activated Verizon LTE SIM and pray it'll work (like how people were able to put an activated sim into a Nexus 7 LTE and make it work before Verizon officially approved it)... Verizon could still block it via whitelisting IMEI numbers...