I have a couple of questions:
I wanted to know if your husband divorces you and takes you back, does he have to give you another dowry?
I also wanted to know if there was any Fatwa on this:
If you live in the West and you have to go to the emergency room in the hospital and you are in pain, can you be seen by a male doctor if the next female doctor wont be available for hours?
I also wanted to know can a wife go out to see her parents without having the permission of her husband? Also does a wife have to stay in the house all the time?
Please get back to me Insha Allah because I am going through the second question that I have written regarding the hospital.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If the husband divorces his wife a revocable divorce (first or second time he divorces her) then it is lawful for him to take her back to wedlock anytime he wishes without paying any Mahr or concluding a new contract as long as her Iddah has not expired. Allah Says (interpretation of meaning): {….And their husbands have the better right to take them back in that period, if they wish for reconciliation…..}[2:228].

But if the Iddah expires, then the former husband cannot return her without her consent and that of her Wali (guardian) and in this case he has to make a new marriage contract and pay a Mahr as this is considered a new marriage.

As for the answer to your second question, you should know that it is unlawful for males to treat alien females and vice versa.  The reason for this prohibition is to avoid exposure of Awrah to alien people and even corporal and physical contact between people who are not Mahram to one another. 

Nevertheless, if there is dire necessity like a disease that can be fatal or a risk of losing an organ if the treatment is delayed then a male doctor can treat a female patient, or a female doctor a male patient.  However, this should be done only in the presence of the woman’s husband or her other Mahrams, or at least some other persons so they would not be staying in seclusion.

Al Izz Ibn Abd Al Salaam says: ‘Covering Awrah is a must.  But the Awrah can be uncovered for necessity like between the husband and the wife and for the purpose of treatment.'

For the third question, it is unlawful for the wife to go out of her husband’s home without his consent.

Ibn Qudamah said in Al Mughni: ‘It is unlawful for the wife to go out of her husband’s home without his permission even if the purpose is to greet her parents or visit them.'

On the other hand, women should not be compelled to stay in their homes all the time.  Indeed, it is lawful for them to go out of their homes in order to satisfy some of their needs.  The wives of the Prophet (Sallallahu Alaihi wa Sallam) as well as the wives of his companions used to go to the mosque and even participate in Jihad, go to the farms, to the market and so on.

However, the woman does not go out of her home without the permission of her husband.  She should also adhere to the ruling concerning Hijab and other Islamic etiquettes and rites.