1: Yes Its supposed to when autotune is working. In the latest version it is most definitely working. However, depending on what your card is doing during an autotune can effect autotune so run it 5-10 times and see which config gives you the best preformace and play around it the -C argument (0, 1,2)
2: Not if you give it a specific config you want it to launch with.
3: Autotune multiple time and find the fastest config then plug in and play with the -H -C arguments and you can normally squeeze out some more extra bits of hash. Plus try adding one or two to the numbers in your -l T config.