Verge Currency wallets feature Tor and I2P networks already integrated, so that there is no additional setup required. Just download the wallet and start transacting with your IP-address obfuscated.
Both Tor and I2P encrypt all network traffic so that a user's IP address and data cannot be accessed. A Virtual Private Network (VPN) also encrypts network traffic, but you must trust the VPN provider to not log any of your activity (which they can and often do). Read this gist for more information about the pitfalls of VPN services.
No, we believe Masternodes are a weakness and centralize the network. A hacker could very easily perform a DDOS (Distributed Denial of Service) attack on the Masternodes, causing the network to be brought down.
If you see "no connection" on your main balance screen, please open the Orbot app and select "apps VPN mode" in the top left menu. A more detailed guide on how to use the Verge Tor Android Wallet can be found here.