Taiwaned answered your question above. I have departed many times from KIX but not arrived there. My impression is that it is a rather sleepy airport, so his experience seems to be accurate.

There is no special queue. I suggest heading to a resident immigration counter (if they have no queue) and explain your situation if the floorwalker tries to stop you. The officer will be indifferent. Or tell the floorwalker (if there is one) that you have a tight connection and he might let you go to the head of the queue.

I have never checked bags on Japanese domestic but I think the deadline is actually 15 min with ANA. With Jetstar it is 30 min and LCCs tend not to be flexible, so I think it's a mistake to use a LCC with a tight connection. If you buy a Starflyer flight via ANA then ANA's rules are in place and you head directly to the Premium check-in area if you are *G. So you could not get a *A award with the domestic leg included?

Also, why are you flying to Narita rather than Haneda if your final destination is Tokyo? You will find many more options to HND in any case. Starflyer does not fly to Narita.