A. Calling a midwife:
One may call a midwife for her from one place to another. [See Halacha 4 regarding when it becomes permitted to call a midwife]
Helping her give birth: One may help her give birth.
B. Desecrating Shabbos for non-essential matters which will calm her down:
Turning on the light: At night one may light a candle for her. [Furthermore] even if she is blind and even if the other women which are assisting her do not require this candle, as they are able to fully assist her without a candle, [nevertheless] one lights a candle for her.
The reason: as although she [the patient] cannot see she becomes more calm upon knowing that there is light here, as she tells herself that if there is anything that she needs my friends can see and can do so for me. However if she were to know that there is no candle here then there is worry that she will become endangered due to fear in her heart, as she will fear that perhaps the assistors are not doing properly what she needs done.
May a relative or friend accompany the Yoledes to the hospital?
First Opinion: Any relative or friend who will help the Yoledes keep calm may travel with them. This applies even if there are other people in the car, such as a medic or EMT, and even if the Yoledes says that he/she does not need the escort of the relative or friend. [However care must be taken to avoid Chilul Shabbos in the process, such as not to carry items with him/her if there is no Eiruv.]
Second Opinion: However there are Poskim which are less lenient and only allow an escort in a case that the Yoledes is asking for one.
Third Opinion: Others allow it in the following cases: a) A first birth even if she says she does not need an escort. B) A 2nd birth and onwards so long as she does not say that she does not need it. C) Even if she says she does not need it by a 2nd birth and on, but she will be left in the ambulance in the care of gentiles. Thus only if it is her 2nd or subsequent birth, and there is a Jewish driver or Medic with her and she says that she does not need an escort should a friend or relative refrain from escorting her.
May more than one person accompany the Yoledes to the hospital, such as her mother and husband?
Seemingly this should depend on how badly the Yoledes wants their company.
May one travel to a hospital of their choice or must it be the closest available hospital?
One may travel to whichever hospital he/she feels that they will receive the best medical treatment or care. However one may not travel to a further hospital simply to save money
May one who traveled to the hospital to give birth and was then released on Shabbos, due to being told that she is not ready to give birth, return home on Shabbos?
It is forbidden for her to drive back home. Although if there is no comfortable area where she can wait until after Shabbos there is room to allow her to have a gentile drive her home, so long as her house is within Techum Shabbos. 
If on Shabbos one traveled to a hospital outside of Techum Shabbos as an escort for a Yoledes, may he/she walk out of the hospital?
Yes. One may walk within 2000 cubits from his destination. If he arrived in a city he has the same Techum as do the city inhabitants.
When traveling to the hospital on Shabbos what items may one bring with him?
All items which the Yoledes will need for the actual birth, even if it is merely to help her feel relaxed and calm, may be brought in all cases. All other items may only be brought if:
- The item is not Muktzah and,
- One is traveling within the city [i.e. within Techum Shabbos] and,
- There is an Eiruv in the cityand,
- The item is needed on Shabbos.
- If one prepared their bag before Shabbos with items that may not be brought, must they remove it on Shabbos prior to leaving?
If there is no time to do so, such as that the Yoledes must immediately go to the hospital, then there is no need to clear the bag. If however time does remain then the Muktzah and other unnecessary item are to be shaken out.
If one is traveling outside of Techum Shabbos must the escorts diminish in the amount of clothing they wear? Such as may the husband take his hat, gartel, kapata?
 So rules Chazon Ish and Az Nidbaru 1/29
 So is implied from Igros Moshe 1/132
 Teshuvos Vehanhagos 2/177
 Piskeiy Teshuvos 330/3
 Piskeiy Teshuvos 330/1
 This includes if one will not be able to pray with a Minyan or eat the Shabbos meals. [Teshuvos Vehanhagos ibid]
 SSH”K 36/10; Teshuvos Vehanhagos 2/174-However there the allowance is only if the gentile is any ways traveling to their area, or one hints to a gentile ambulance driver to do so. However to ask a regular gentile to drive them back he does not allow.
 Based on 407/1
 As this is similar to a midwife which has traveled to help a woman give birth. Likewise the escorts are also considered to have traveled due to Pikuach Nefesh. Now although in 405/5 Admur rules that “when one left the Techum due to Ones then if there is a Kosher Eiruv in the city one may walk anywhere in the city. If there isn’t a Kosher Eiruv in the city, then one may not leave the hospital building for any purpose.” Nevertheless in a case that one left to help save a life the Sages did not limit them to their 4 cubits even if there is no Eiruv in the city.
 Tzchebiner Rav answer to Rav Gerelick of Kfar Chabad