No, no internet connection is needed. Your Gen 3 will broadcast a WiFi Signal that your tablet/phone/whatever will be able to connect to. That WiFi signal is only good for connecting to the device.
If you have a Gen 2, or Gen 2 touch model, you can purchase the "Go Free Wifi 1" module. It is basically a wireless router that connects to your Gen 2 or Gen 2 touch. Same principle as the Gen 3 it is just they included this technology right in the unit.
My understanding is that you can view the display of a Gen 3 with a phone connected via Wifi but you cannot control it. If you have a tablet or IPad, you can actually control the display (gen 3 model). For a "non touch" gen 2 model, you can only view it if you have the Go Free module.
The second part of your question is tricky but... IF you connect your device to WiFi, you are basically turning OFF your digital transmission signal (connection to a cell tower). You are only picking up the access that the WiFi hotspot you connect to is broadcasting. Because the WiFi hotspot on your Gen 3 device is NOT connecting to the internet, connection to the WiFi signal on your Gen 3 in turn makes your tablet NOT able to connect to the internet while connected to the Gen 3. There are some settings you can change however that can allow you to do both.
My understanding is that Lowrance/navco is looking at creating a WiFi hotspot (in the future) that will allow you to use it just as you would at an office or home. Connect to it, view the fish finder, and also provide a connection to the internet.
Hopefully this answers your questions.
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