Can I buy an unlocked phone from an outside (not Verizon) source to use on Verizon account?
Technically yes and no. You can buy any device you want, even if its not a supported Verizon device and use it on the network but your mileage may vary. You may not get updates and enhanced features. What phone are you considering?
These phones will work with the Verizon Wireless network.
Nexus 6P - Solid Metal Frame - Huawei - Nexus - Android Phones - Google Store
Nexus 5X - Fingerprint Scanner - LG - Nexus - Android Phones - Google Store
Moto X Pure Edition (2015) - Unlocked Smartphone - Motorola
if you buy an unlocked device like from apple, which is what i did, it will work android device im not 100% sure on but my phone can be used on any carrier pretty much