Does BasicTalk Service Offers Internet Connection?

There is no such service called  Basic Talk Internet. Basic Talk Internet Phone Service is a VoIP (Voice Over Internet Protocol) based internet phone call service. It works based on your internet connection offered by the Third Party and not by BasicTalk. BasicTalk does not offer a dedicated Internet Service. 

You can use any service like DSL or Cable internet to actively use the VoIP based phone service offered by BasicTalk.

For your information, an organization that offers internet connection is called ISP (Internet Service Provider). You can subscribe to their monthly or annual plan to gain a highspeed internet connection. Once you have a modem that offers the highspeed broadband connection, you can opt or signup for BasicTalk Account.