1) I should use two separate 12-14 AWG dual cables from the circuit breaker to the power molex connector on the ICOM so that all four power connectors are in use.
No. You only need a two conductor cable and size 12 is not adequate. The size cable you need depends primarily on how long the cable run is from battery to radio. Like Bill says, use #6 which is good up to 15 feet. You need this size because of voltage drop, not because of it's current handling capabilities. I also suggest running directly to the battery with in-line fuses. Place a heavy duty terminal board near the radio to connect the #6 wires and the wiring from the molex plug.
2) If I just use the power pins ( +/-) from the SG-230 to the M-700 the SG-230 will still tune and "remember" the frequencies, it will just disable the tune switch on the Icom.
a) If I attach the KEY and START pins from the ICOM to the RED-WHITE reset lock wire from the SG-230 I can use the tune Key on the front of the ICOM it just won't have fast response unless I put in line the capacitor and resistor.
No. You must use the capacitor/resistor but I don't recommend using this method at all. It's not worth me trying to explain how this all works but suffice it to say that your radio could give you a successful tune indication when in fact this is not the case.
b) I I attach only the power pins on the ICOM to the power leads of the SG-230, I can also attach the BLACK-WHITE wire from the SG-230 to an off line LED and it will light when the frequency is tuned (sort of acting like the light on the front of the M-700 called TUNE.
Yes, this is what I recommend. You can use the +12v of the ICOM to not only power the tuner, but also to connect to one side of the LED with the black/white wire from tuner to the other side. If you do not use a "12 volt LED", then you must put a resistor of around 560 ohms in-line with the power lead to the LED. Here's my Icom M710 shop radio that uses an SEA tuner which is much like the SGC. Notice the red LED above and to the left of the swr meter. It will only come on if the tuner has successfully tuned giving you a clear indication that it has done so.
c) Finally - I am not sure I understand the blowing in the Mic recommendation. Are you saying that if I only connect the power cables between the SG and the ICOM I need to activate the SG by blowing in the mic even if I only want to receive and not transmit?
Blowing into the mic is not sufficient, you must talk or whistle until the tuner is tuned. You will significantly improve your receive signal if you tune the tuner on the band you want to receive on. Generally, once tuned on a band, say 8Mhz, if you change frequencies within that band the tuner will not need to re-tune.