Yea there is no Chrome app but you can see your BTG balance by installing the BTG app on the ledger, open BTC chrome app and open the BTG app on the ledger opens the BTG balance.
As far as I know, that might be the reason why you can't send it.
For the connectivity issue, what's the OS that you use? Have you tried changing the cable or USB port? Can it shows other coins balance and interact with it?