Is it permissible to pray Asr combined with Maghrib due to lack of time, and is it permissible not to repeat the Fajr Sunnah prayer when in doubt about having concluded it?

The questioner erred by missing the Asr prayer. She is obligated to perform it immediately upon waking up, as the Prophet, peace and blessings be upon him, said: "If one of you oversleeps or is heedless of a prayer, he should pray it when he remembers it, for Allah says: 'Establish prayer for My remembrance.'" Repentance is obligatory for this grave sin, as a severe warning has been reported against those who miss the Asr prayer.

As for the doubt concerning the taslim (salutation of peace) at the end of the prayer, the taslim is a pillar (rukn), and whoever doubts a pillar must perform it, unless they suffer from obsessive-compulsive disorder (waswasah). The questioner's statement that she completed the prayer "as if she had saluted" is unclear in meaning, because the taslim is the last act of the prayer.