The said covenant (ahd) is correct and one should act upon it if the profession is required to prevent harm from reaching Muslim women. It is not obligatory to act on it if there are enough Muslim female physicians. It is permissible take up such a profession, and it is permissible to deliver babies when necessary.
If it is an unconditional grant, not pursuant to any loan contract, then it is permissible to take it.
Yes, you can.
It is permissible to do so if it does not involve another prohibition.
If the prayer was not offered because the person was asleep, then a sin is not committed, but the person has lost the great reward that Almighty Allah promised for offering prayers on time. In a narration the Messenger of Allah (peace be upon him and his progeny) said: â€œMy intercession will not be granted (on the Day of Judgment) to whoever delayed performing the obligated prayer until after its designated timeâ€.