The voltage across R2 is 5.0 V; to find the resistance of R2 you need to find the current through it next.
Hint for E3.6
Refer to E2.6.
You may assume a particular voltage and current (or power) if you wish, but the fractional increase of surge current should be independent of those particulars. For example, you may consider a typical room lamp (100 W, 115 V) or the flashlight lamp from the laboratory exercise (3.0 V, 0.32 A). if you would like some numerical values with which to work.
Hint for E3.12
Nodal analysis works OK; consider the equivalent resistance of the two 10 ohm resistors.
For mesh analysis as we have been setting it up, you may wish to interchange the 20 ohm resistor and the 1 A current source in your drawing.
Source substitution works great! Replace the 1 A current source in parallel with the 20 ohm resistor with the equivalent Thevenin generator and the answers appear as if by magic...