Inconsistent results measuring current
To measure current with a series resistance, you would use your multimeter as a voltmeter and measure the voltage across the resistor.

Your drawings show a resistor in series with your meter, and the notes say that you are making measurements with voltmeter and ammeter.  When you measure the voltage, you get the same result as measuring the voltage directly.

Connect the 10 ohm resistor to the solar panel so that the circuit is complete.

Measure the voltage across the resistor.

Now \$E=IR\$ so \$I=E/R\$  so divide the measured voltage by 10 to get the current.

It would greatly surprise me if yoy get anything like 120uA.  That value that you have measured looks wrong to me.  A solar cell that only delivers 120uA would be very weak - there's not much you can do with that little current.

I think you are probably measuring current wrong.  Most multimeters require that you plug the red lead into a separate jack to measure current.  Double check your connections, and see if you get a more reasonable amount of current.

To measure current, you would usually want to measure it while your solar cell is powering a load.  What you are measuring is the short circuit current.  That's the maximum current it can deliver, but it is at the minimum voltage.



Since you aren't sure what "parallel" and series are, try this:

Connect the resistor from the + to the - of the solar cell.

Connect the multimeter red lead to the solar cell +, and connect the black multimeter lead to the solar cell -.  

Your multimeter is now in parallel with the resistor.