1.a. Nope
b. Only to passive thermal sensors, as the engines are basicly shut down and so do not emit any heat
2. See Erik´s reply
3. There simply is no correct answer. Aurora allows soooo much variety, you can´t predict anything. Your enemy may fly around in a huge battleship wich would have a thermal sig of 3000, but has engines with thermal reduction 25%, so only has an effective sig of 750. A destroyer (typical thermal sig of 400 to 600 (assuming some 5000 to 7000 tons and 3000 to 4000 km/s speed) would then only have a sig of 100 to 150, or he just shuts his engines down, you loose any lock instantly.
Thermals vs. missiles? Forget it!
Thermals vs. fighters/FAC? Very hard, thermal sig is _very_ small (I am tempted to say: vs. fighters forget it too), so you need big sensors, making the missile _very_ ineficient.
Thermals vs. warships? Can work, but see above.
Personally, if I use sensors on missile at all (rather rare) I go for actives, as they do not depend on the enemy to comply with my wishes.
In those cases, I go with the rule of thumb to have at least as much sensor range as my missiles fly in a single 5 second tic, i.e. a 30000km/s missile will mount a 150000km ranged sensor.
This rule of thumb can be applied for passive sensors too, of course. If you´re enemy uses ships with a thermal sig of 800, you designe the sensors of your missiles accordingly.
Note: The term "destroyer" realy tells nothing in Aurora, as you can class a 800 ton gunboat or a 100000 ton behemoth a destroyer.