There is nothing wrong with one praying in the bedroom. The Prophet used to offer optional prayers and Qiyam Al-Layl in the rooms of his wives.

If the Mu’dhdhin gave the Adhan for prayer on time and was not late in doing so, then you offered the prayer before it was due, so you have to repeat that prayer.

If the traveller in a plane wants to offer a Sunnah prayer, then he does not have to face the Qiblah. However, when praying an obligatory prayer, it is essential to face the Qiblah and to bow and prostrate if one is able to.