When you see a variety of different errors in a short period of time like this it typically indicates that there's an issue with the connection along the route that traffic is taking from your console to Bungie, or the P2P connections Destiny utilizes to connect you to other players. Are you using WiFi? If so, please try switching to a wired connection temporarily. This is an important first troubleshooting step to rule out wireless signal strength/stability as a possible cause.