If a woman is in labor before Shabbos, must she go to hospital before Shabbos, or can she wait until she is ready and then go on Shabbos?

It will largely depend on whether the driver will be a Jew or gentile. If the driver will be a Jew, normally, we would say that since she knows before Shabbos that she requires to be hospitalized on Shabbos, we would want her to avoid the unnecessary violation and go to hospital before Shabbos. [1]

However, if for example there is doubt as to whether the birth will be on Shabbos and if she did go to hospital before Shabbos, thus having to spend most of the Shabbos in a foreign and sometimes awkward environment, we would say that she need not sacrifice her mitzvah of Oneg Shabbos (enjoying the Shabbos) in order to avoid traveling on Shabbos, as when she does travel on Shabbos, it will be for the sake of pikuach nefesh. [2]

What if one must sign a consent for surgery on Shabbos?

Obviously when surgery is necessary on Shabbos it must be a case of pikuach nefesh, or even a safeik pikuach nefesh (doubt) and as such everything should be performed to facilitate for surgery. In some countries, the patient or his representative is required to sign documents, failing which the surgeons will not operate. Accordingly one may sign.
However, since signing the documents is not a direct act of pikuach nefesh, everyone agrees [3] that if it can be done b’shinui it must be done b’shinui, because in that way it will downplay the melacha of writing from a d’oraisso to a d’rabanan.

How is the shinui implemented?

The basic shinui with regards to writing is to write with one’s left hand. [4] Another option is to scribble a signature, as it is common knowledge that many people scribble something for a signature, and when the scribble is not comprised of letters or specific shapes it would not be called “writing” mid’oraisso. (One might even “scribble” with one’s left had, thereby minimizing the issur even more).

How is one to walk through the electronic doors?

Devices that sense your presence are either bouncing some wave off your body or are passively detecting waves that you emit or reflect. The wave-bouncing detectors emit high frequency (ultrasonic) sound waves or radio waves and then search for reflections. The door is opened when changes in the intensity or frequency pattern of the reflected waves are detected. Passive detectors look for changes in the infrared or visible light patterns reaching a detector and open the door when they detect such changes. Therefore, one is normally forbidden to open such a door on Shabbos. In a case of a dire emergency and one must enter a hospital through such doors, one may do so without hindrance. When it is not an emergency but a case where the patient must be admitted to hospital, the best alternative is to request a gentile to open the doors.

One cannot argue and say that since one does not open the doors with one’s hands that it is called a shinui, because the regular method for opening the doors is designed to operate ultrasonically.

If I merely wish to visit an ill person in hospital and the only way to enter is through electronic doors, may I do so?

You yourself may not activate the system to open the doors but you may ask a gentile to open the doors for you, when your presence is needed for the wellbeing of the patient. This is based on the halacha that a gentile may even violate an issur d’oraisso for the sake of an ill person on Shabbos. There is room for speculation whether the choleh (ill person) needs every visitor, but when the aid is needed it would be permitted.

If a Jew activated the electronic doors in a forbidden manner (not for a choleh), i.e. when it is not for pikuach nefesh such as at a hotel entrance, may I enter once the doors are open?

The basis of the question is that since one may not benefit from another Jew’s chilul Shabbos (violation of the Shabbos) [5] is walking through the open doors considered benefiting from the chilul Shabbos?

We can learn from a similar case. If one opens a package or a bottle in a forbidden manner, the contents of the packet or bottle may be consumed. [6] Part of the reason is because the actual contents were not altered or modified by the issur and thus it is not prohibited on account of the issur. In this case as well, since one is not benefiting directly from the Shabbos violation, because being in the hospital is an indirect benefit of the fact that the doors are open, one may pass through the doors.

However, other poskim say [7] that if without the Jew, the doors would not have opened, one may not pass through the doors when opened by a Jew.