Two power supplies to one feed
The power supply seems to be capable of driving the whole strip chain.

If you run the supply from only one end of the chain, there will be voltage drops. Because, first strip draws 3A and the remaining 15A flows through its copper tracks. Then second strip draws 3A and the remaining 12A flows through its copper tracks. Then third strip draws 3A and the remaining 9A flows through its copper tracks ...and so forth. This means, there will be a couple of voltage drops on the strips which results in brightness decrease from one end to another. That's why the supply should be applied from both ends.

1) The current need of cables for each option is about 9A. According to the table on this page (http://www.engineeringtoolbox.com/wire-gauges-d_419.html) at least AWG #16 will be sufficient. 

OPTION 1:
If you use AWG #12, the cable resistance of 50ft will be 0.08ohms and the voltage drop on each cable will be about 9A x 0.08 = 0.75V. So, input voltage on the strings will be about 12 - (2 x 0.75) = 10.5VDC. This will cause a decrease of brightness, clearly.

OPTION 2:
If you use two separate power supplies and make the connection cables shorter, this will give you a better result (i.e. nearly no voltage drops on the cables).

Note that there will be a little and equal amount of brightness decrease on LED3 and LED4.

2) If you run the power supply from both ends of the strip chain (OPTION 2 with one supply or two), strip 3 and 4 shouldn't be connected to each other. Because you apply the supply voltage from both ends.