What should I do concerning the 'Asr or Fajr prayer if its time has passed due to compelling circumstances, and should I pray it after its time has passed, knowing that praying after sunrise is disliked?

The prohibition of praying at sunset or sunrise does not include obligatory prayers. Whoever misses an obligatory prayer must perform it immediately when able, for the Prophet, peace and blessings be upon him, said: "If one of you oversleeps or is heedless of the prayer, he should pray it when he remembers it, for Allah says: 'Establish prayer for My remembrance.'" And being in a means of transport is not an excuse to abandon prayer until its time has expired.