Good questions.
1. All resistors should be 0.5 watt metal film, 5% tolerance or better (metal film resistors are normally 1% anyway), except for the two 0.33 ohm resistors, which should be 5 watt wirewound 5%.
2,3. No, the recommended way to adjust the quiescent current (measured as the voltage between points E and F) for a class AB power stage is to keep readjusting it until it's close to (within say 5~10% of) the desired current when the heatsink temperature is stable. Wait at least 5 minutes between each adjustment. Each time you adjust it, the heatsink temperature will change, and after 5 minutes you'll see that the current has gone in the other direction from the previous adjustment, but by a smaller amount, so you're getting closer to the correct setting each time.
4. Actually I think you should use one with no crossover distortion in the output stage, such as MC34071. If you have trouble finding the MC34071 in a through-hole package, you may find it easier to get the MC34072, which is just the dual version.
No worries.