My Pi 2 is sitting in front of me with an HDMI cable, Ethernet cable and Logitech unifying receiver plugged into it. I have a USB meter between it and the wall wort that shows it using about 250 mA. (These meters are under $10US on Amazon.) With a fully charged 1200 mAH battery I would expect it to run 1200/250 => 4.8 hours. You'll need something bigger to get you through the night. Things that could affect this estimate:
* Difference between rated battery capacity and what you actually get (efficiency)
* Difference in load for your Pi 2 - depending on what's plugged into it and what it's doing.
* Benefit from indoor lighting - depends entirely on your solar panel and how bright the lighting is. Might reduce battery draw a little.
If this system is unattended overnight you can see how long it runs with your present setup and gauge what you have to do to get all night operation. This little shell script will update the timestamp on the indicated file every 5 minutes (300 seconds) until the system dies. It's not really good to shutdown that way so backup your files first in case it results in corruption. (Most of the time any corruption is automatically fixed on the next boot.)
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leave the 'sleep 300' part or the script will generate a lot of disk I/O activity and use more CPU. I tried it for a bit and it drove CPU usage to 27% and power usage to ~400 mA.