Is it permissible for a Muslim woman to offer herself to the Prophet, peace and blessings be upon him, as a bondwoman or wife after his death, and to remain unmarried in this world so that she may attain the Prophet, peace and blessings be upon him, in Paradise?

It is not permissible for a woman to forgo marriage in order to attain the honor of marrying the Prophet, peace and blessings be upon him, in Paradise. Such an act is a blameworthy form of asceticism (tabattul), and there is no way to achieve it. The wives of the Prophet, peace and blessings be upon him, in Paradise are his wives in this world, along with the Houris. Whoever loves the Prophet, peace and blessings be upon him, should obey him, for whoever obeys him will be with him in Paradise, as Allah Almighty says: "And whoever obeys Allah and the Messenger - those will be with the ones upon whom Allah has bestowed favor of the prophets, the steadfast affirmers of truth, the martyrs and the righteous. And excellent are those as companions." [An-Nisa: 69], and as the Prophet, peace and blessings be upon him, said: "You will be with whom you love." Part of the implication of love is to emulate him in marriage, for it is the Sunnah of the Prophets.