Connecting mobile battery and LED bulbs to 10.5v Solar cell
You need a lot more than just a resistor.  You need something to control the current flow through the LEDs.  That could be as simple as a bunch of resistors, but a constant-current supply would be more efficient.

You need a proper charging circuit for the battery.  Put 10.5V across a normal phone battery, and there's a chance it will catch fire.