Prayer

You can pray Immediately after the adhan.

If you know you can rush it and join in time before the Imam begins his prayer, do so. Otherwise, break it!

Yes, this is recommended.

You follow the time table of your position while flying. It is the sun that tells you the prayer times and not the watch on the ground.

This is permissible.

You should say it even if he doesn’t unless you are the only one and people would be irritated from that. In this case, don’t say it but look for a masjid that follows the sunnah.

The prayer is valid but you must clean yourself first and perform wudhu for every prayer.

Due to your ignorance, the prayer is valid. However, you shouldn’t have continued with the second prostration. You should have also offered two prostrations after Salam for adding something which was not part of the prayer.