There are two scenarios that will have different outcomes:
A mode S transponder only transmits when it is pinged with an SSR signal. If the transponder is set to 7700 and the aircraft is not under radar coverage, no one will receive the signal as nothing will get broadcast. So in short only aircraft in radar range are capable of being "heard&...
Terrestrial radar systems only cover so much area. The latest Terminal radar system the FAA uses, the ASR-11, has a working range of 60 nautical miles. The Enroute ARSR-4 has a range of 250 nautical miles. The trade-off is between update time and range; a radar antenna that spins faster can provide quicker updates, but only in a smaller radius.
It is very ...
At low altitude engine loss you have no choice but to land straight ahead. Anything but the slightest heading adjustments will most probably end catastrofically. Your memory items are (at least, depends on complexity of aircraft):
Gently but decisevily lower the nose
Close fuel valve
Adjust airspeed for landing
Flare and land
How do you determine if you have enough runway ahead? That's a tricky one, and in this situation you quite possibly have milliseconds to make that determination. It's going to be an estimate at best because you certainly wont have time to do any calculations. As a general rule I'd say if you have around half the runway length left you're probably good.