Short answer: Up to 7 years at 1 daily update. Around 1-3 years generally with other configurations and applications.         
Long (more accurate) answer: It depends on many things, see here for details along with a battery life calculator. 

See How to change the update rate on the Oyster2, Remora2 and Yabby        
The Oyster2 has 3 tracking modes, discussed here - Battery Powered Devices - Overview of Operations        

The tracking modes are:

• "Standard" GPS Tracking. Movement based tracking. The update rate is increased when on the move (as according to the GPS - i.e. we're actually covering distance)
• "Jostle Mode" - accelerometer Movement based tracking, the update rate is increased when accelerometer activity is detected - even if we are sitting in one spot vibrating. 
• Periodic Tracking - just update twice daily etc.

Yes, see Scheduled Uploads. 

See Oyster2 - Getting Started

By default, the Oyster2 is setup for trip tracking. The following default settings apply:

• Out of Trip: 12 hour heartbeats. This is a GPS point and an upload every 12 hours.
• In Trip:
  • Start trip threshold of 250m
  • Upload on trip start.
  • GPS points every 2 minutes
  • Upload every 30 minutes.
  • End a trip after 5 minutes of no movement.
  • Upload on trip end.

It is most likely that the device simply failed its first fix attempt (it will attempt one on start up) - if it fails, it will go back to sleep until the next scheduled upload. On default settings, this means not for 12 hours, unless you move over 250m from your position (to start a trip). So to attempt another, move to a location with good GPS reception, remove the batteries for 30 secs, and reinsert. This does not do anything special, but it reboots the device and will mean it will start up and attempt another fix and upload.     

For further troubleshooting steps see:

• GPS Troubleshooting
• How to 'force' a connection

Run hours can be tracked quite accurately using Jostle mode, see here for information: Battery Powered Devices - Run Hour Monitoring.    

Odo readings are not as simple. Generally hard-wired devices should be use to track odometer readings. Getting an accurate reading relies on getting positions frequently enough during movement. The default 2 min logging can sometimes be OK, but it will never be as accurate as a hard wired device which will keep the GPS on during movement, getting a location more frequently and following every corner. The Oyster2 will clip corners, or you can imagine in the extreme case, if you make a round trip between two GPS fixes and return to your start point, the distanced travelled will be 0m according to the Oyster2.

See here: Common Concepts - Recovery Mode

See Alert on After Hours Movement

See HERE

For integrators, the remaining battery % is reported in Analogue 6, in the analogue data field.

Yes, see Common Configurations - High G Events
The accelerometer enables a few useful firmware features, see here: Accelerometer Event Detection - Accident, Rollover, Tilt, Tip and Rotation Counting