The difference between the 1377 and 1378 variations of the GTX 460 FTW edition is all in the cooler. They have the same clock frequencies.
 
Before I get to your questions, here's a quick Pros/Cons list of Reference vs External Exhaust cooling on the FTW card.
 
Reference

• Pros: Run cooler, run quieter
• Cons: Requires a case with good airflow, fan blades are known to break off

External Exhaust

• Pros: Heat is pushed out the back
• Cons: Tend to run louder and hotter

Warranty does not matter for either design, because the warranty is the same between 1377-TR and 1378-TR.
 
Now in regards to your questions...
 

1. In my opinion, 1377 has the better cooler. It has what's classified as a reference style cooler. As I said before, it typically runs cooler and quieter. However, a few members have posted around here about fan blades breaking off, which requires a full blown RMA to the US. This may be a hassle if you live outside of the US.
2. 1377, the reference cooled 460 FTW, typically has better temperatures.
3. Both cards consume the same amount of power at stock settings.
4. External exhaust means that the heat from the card is exhausted externally; the heat gets pushed out the back. In contrast, the reference cooled card pushes some heat out, but the majority is pushed back into the case.
5. See my chart above.

If you have any more questions, just post again.