Hello Aerotech
I'll try my best to answer and then leave it for anybody else to add.
Can APU start automatically in case of autostart?
Don't know of any aircraft that has an automatic start on APU. You might be outside APU start envelope.
In case of inflight engine flame-out (engine out of the envelope), will the pilot use the crossbleed, dive (to have more speed), or use the APU?
On most aircraft there are certain envelopes for different types of starts.
On a twin with one engine running while in the air, you would probably go for crossbleed start. (On my a/c, CRJ, this is actually your only option)
With double engine failure, you can only do APU start below FL130, so above that you will try windmill start. You need 300KTS plus, so you need altitude to accelerate and maintain that speed. Once you have one engine running, you will do crossbleed start.
I might misunderstand your use of the word "autostart". You have continuous ignition, which just runs the igniters continuously. I don't know of an a/c where the engine restarts automatically.
You also have a crossbleed start altitude limit and the pilots will know it well. If you are at altitude, you have time at your disposal, so it is not important to get engine going immediately. (You will be losing cabin pressure, so you probably won't glide from FL330 to FL150, where APU can run aircon packs, at best glide speed - you can just as well use altitude for windmill start)
We practice double engine failure in sim every year, especially after Pinnacle CRJ accident.
The actions would be the following:
1. Continuous ignition on.
2. If engines continue to wind down - set up for glide until in windmill start envelope.
3. Start APU
4. When ready (and in envelope) - accelerate to 300+KTS and attempt windmill start on both engines.
5. If that fails, try again until at FL130 (you can also just glide and wait for FL130)
6. From FL 130 try APU starts until you run out of altitude or until you get one running.
7. Once you have one going, you can fly, so the rush is over. You then have time to try crossbleed for the other one.
For the knowledgeable - I have obviously left out all the other little actions in the checklists - this is more a sequence of events.
I hope this helps.