Answer 1) A. Replacing the home button flex will disable usage of the Touch ID sensor (read more here) B. It will not help with the charging port. Answer 2) Normally I would assume that likely the reason the iPhone would not charge is due to the dock connector flex being slight unplugged. However, the fact that your phone will still register the touch ID input leads me to believe that the connection is secure. Is there any damage to the surface mounted components on the mainboard by the battery connector? Do all the resistors next to the battery connector appear to be there (you can use this image for reference)?
One possible solution is a hard reset. This can be performed by holding the power and home button simultaneously until the phone turns off and the Apple logo appears. If that does not resolve the issue then the next step would be trying a new LCD/Digitizer.
There is no way to enable a disabled iPad without a computer. If you can use a friend or family members internet enabled device and can access www.icloud.com/find it is possible to remotely erase your device by following the instructions below. The following instructions are from Apple's Support Website If you set up Find My iPhone on your iOS device or Mac, you can use iCloud to erase and restore it. 1. From another device, go to icloud.com/find. 2. If prompted, sign in with your Apple ID. 3. Click All Devices at the top of your browser window. 4. Select the device you want to erase. 5. Click Erase [device] to erase your device and its passcode. 6. Now you can either restore from a backup or set up as new. If your device isn't connected to a Wi-Fi or cellular network, you can't erase it with Find My iPhone.
Unfortunately there is no sure -fire way to test the components you listed with out a functional LCD and Digitizer. The fact that the phone still rings is a good sign. It means that the phone is still on, the cellular modem is functional, and the speaker works. Given the fact that the speaker connects to the mainboard via the same flex cable that the microphone is on, there is a good chance that the mic still works. My advice is to open up the device and take a look at the components. Look for any physical damage to the mainboard or flex cables. Also, check the battery and make sure it has not begun to swell. Sudden impact to the battery such as a car running over it may cause it to begin to swell up. In my experience the G2 is pretty resilient. So, if everything looks good on the inside, go ahead and get a new screen.