Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
A pregnant woman has iron deficiency. When she showers, she becomes very tired and feels cold. What is the ruling on tayammum in this situation?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
One should not resort to tayammum (dry ablution) as a substitute for the obligatory ghusl (ritual bathing) so long as it remains possible to use water — for example, by heating the water, warming the place where the bathing takes place, or taking other similar precautions. However, if such measures prove ineffective, or are simply not possible to carry out, and performing ghusl [with cold water] would result in severe harm, then tayammum becomes permissible in that case, due to genuine inability to use water on account of the harm that would result, as described in the question. That said, she must make up (qaḍā') the prayers she performed using this tayammum.
It is stated in Bushrā al-Karīm: "One should not perform tayammum on account of cold unless warming the limbs fails to remove the aforementioned harm, and no means are available to heat the water — such as a vessel, firewood, or fire — and one fears [that using cold water would result in] any of the harms mentioned earlier in the discussion on illness: danger to life, loss of function in a limb, the onset or worsening of an illness, delayed recovery, or the [visible bodily] blemish mentioned in that discussion on illness. In such a case, tayammum becomes permissible due to the harm involved, but the prayer must still be made up afterward (qaḍā'). If, however, warming the body proves effective, or the means to heat the water are available, or none of the aforementioned harms are feared — then tayammum is not permissible, even if using the water causes some degree of discomfort or pain, since mere discomfort alone does not permit resorting to tayammum." And Allah, the Exalted, knows best.
Is the prayer of a woman who is led by an Imam via T.V. permissible?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Amongst the conditions for the validity of prayer is that both the Imam and those led by him must be in the same place. Thus, the prayer of the person who is being led by a televised Imam is invalid unless he/she was with him in the same mosque. And Allah Knows Best.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.