1) There may arise situations where there is ample water but using it for wuzu might scarce that water originally kept for drinking or other purposes [1].

2) Yes, it can be done over shoes. Refer to the above video from 1:49:18 to 1:50:05

3) It is ijtihaad of Prophet Muhammad (sws) based on the guidelines provided by Quran. Therefore, there is no reason to reject it just because it is transmitted through Akhbar-i-Ahad. Had it not been present, a rational scholar would’ve had to do this ijtihaad on his own based on the same guidelines of Quran.

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[1] If, in the case of a journey, sickness or unavailability of water, wudu and the ceremonial bath become difficult, in the verses of Surah Nisa(4:43) and Surah Maidah (5:6) quoted above the Almighty has allowed the believers to do tayammum (dry ablution). The verses go on to state the method of tayammum as well: hands should be rubbed on a pure surface and wiped over the face and hands. It is reported about the Prophet (sws) that for this he struck both his hands on mud and blew on them and wiped the left hand on the right and the right hand on the left and then wiped both hands on the face. [13] The Qur’an has clarified that the tayammum suffices for all type of impurities. It can thus be done both after things that terminate the wudu and after states which need the ceremonial bath. Similarly, it needs to be appreciated that in case of being on a journey or being sick, tayammum can be done even if water is available. Writes Imam Amin Ahsan Islahi:

… in case of sickness, the ceremonial bath and wudu can cause harm and thus this relief was given. Similarly, in case of being on a journey, a person may encounter circumstances in which he might have to limit himself to tayammumonly. For example, water may not be available in large quantities. In such cases, using it for bathing etc might leave it scanty for drinking or there could be a chance that if a person starts preparing to have a bath he might be left behind from his fellow companions of the caravan or a situation may arise when having a bath may become very difficult in a train, ship or aero plane that a person is travelling in. [14]

The Prophet (sws), by drawing an analogy with this directive of tayammum wiped his socks and turban [15] instead of washing the limbs they are worn on. He also allowed people to wipe their socks if they are worn after doing wudu. For a stationed person this was allowed for one day and for a traveller for three days. [16]

Another relief given by the Prophet (sws) on the basis of this analogy was that if the hair of women is plaited, then pouring water over it without disentangling it was enough. [17] Still another relief on this basis was that if states which require the ceremonial bath to become pure take the form of sickness, then the ceremonial bath can be done once and other prayers can be offered without it as well. [18]

(Excerpt from Meezan: Javed Ahmed Ghamidi)

(Translated by Dr. Shehzad Saleem)

[13]. Al-Bukhari, Al-Jami‘ al-sahih, 59, 61, (nos.338, 347); Abu Da’ud, Sunan, vol. 1, 85-86, (nos.321, 322).

[14]. Amin AhsanIslahi, Tadabbur-i Qur’an, vol. 2, 303.

[15]. Al-Bukhari, Al-Jami‘ al-sahih, 36, 39-40, (nos.182, 203, 205); Muslim, Al-Jami‘ al-sahih, 127-129, (nos.622, 633).

[16]. Muslim, Al-Jami‘ al-sahih, 130, (no. 639).

[17]. Ibid., 146, (no. 744).

[18]. Al-Bukhari, Al-Jami‘ al-sahih, 42, 53-54, (nos. 228, 306); Muslim, Al-Jami‘ al-sahih, 147-148, (no. 753).

It is a matter of ijtihaad. If you feel like it doesn’t make sense then don’t follow it.

But I see socks and shoes in effect forming one-unit because at times, the effort (‘Mushaqqat’) required to take off shoes could become the actual reason for Masah.

You can do Masah over socks in winters as this Ijtihad was done by Prophet Muhmmad (sws) Himself and whose reasoning can be very well understood along with its basis provided in Quran. For rest of the scenarios, we have to do ijtihaad and decide for ourselves keeping in mind the level of difficulty that we are truly facing in those situations. For further understanding of the concept, please refer to the video provided above once again.