She works as a nurse on the maternity ward and she has some questions about purification and prayer

Firstly: 

One of the conditions of prayer being valid is the body and
clothes being free of impurity. If any impurity (najaasah) gets on to the
body or clothes, it is essential to remove it before starting to pray. 

Your mother can set aside clothes for prayer and clothes for
work, then when she wants to pray she could take off the work clothes and
put on the other clothes. 

Or it is enough for her to wash the place where the impurity
is on the clothes, then pray wearing them if she wants. 

Please see the answer to question no.
12720 and
125879. 

Secondly: 

Wiping the head with water during wudoo’ is one of the
obligatory parts of wudoo’. But if a woman is wearing a head cover, she does
not have to take it off and she may wipe over it, especially if it is
difficult to take it off. Al-Bahooti (may Allah have mercy on him) said:
Wiping over a woman’s head cover is valid, especially one that is wrapped
around the chin, because Umm Salamah used to wipe over her head cover, as
was mentioned by Ibn al-Mundhir, and the Prophet (blessings and peace of
Allah be upon him) said: “Wipe over the khuffayn (leather slippers) and the
head cover.” Narrated by Ahmad. And because it is a covering that is
difficult to remove.

End quote from Daqaa’iq Ooli al-Nuha, 1/62. See also
al-Mughni, 1/187 

The hadeeth “Wipe over the khuffaayn and the head cover” was
classed as da‘eef (weak) by Shaykh al-Albaani (may Allah have mercy on him).
See Da‘eef al-Jaami‘, no. 1270. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: Is it permissible for a woman to wipe over her head cover? 

He replied: The well-known view of the madhhab of Imam Ahmad
is that she may wipe over the head cover if it is wrapped around the chin,
because that was narrated from some of the women of the Sahaabah (may Allah
be pleased with them). 

Whatever the case, if there is any difficulty involved,
either because it is cold or because it is difficult to take it off and put
it on again, that there is nothing wrong with wiping over it in this case,
although it is better not to do so.

End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen,
11/171. 

Thirdly: 

The basic principle is that it is not permissible to delay
prayer until the time for it is over, except when one has an excuse, because
Allah says (interpretation of the meaning): “Verily, As‑Salaah (the
prayer) is enjoined on the believers at fixed hours” [al-Nisa’ 4:103].
This has been discussed in the answer to question no.
21958. 

What is required of the sister who is asking this question is
to take all possible measures to offer the prayers on time. If that is too
difficult for her or she is not able to do it because of the way her work is
organised, then there is nothing wrong with her putting two prayers
together. So she may put Zuhr and ‘Asr together, and put Maghrib and ‘Isha’
together, at the time of the earlier or later prayer, according to what is
easiest for her. 

The scholars of the Standing Committee for Issuing Fatwas
were asked: Is it permissible to delay prayer until the time for it has
ended, such as ‘Asr prayer, in the case of necessity, namely if a doctor is
doing surgery and if he leaves the patient, even for a short time, that will
pose a danger to his life? 

They replied: The doctor who specialises in doing surgery
should take care to do surgery at times when he will not miss out on
offering the prayers at the proper time. In cases of necessity it is
permissible to put two prayers together at the time of the earlier or later
prayer, such as putting Zuhr and ‘Asr together, or Maghrib and ‘Isha’,
according to what is dictated by necessity. End quote. 

Fataawa al-Lajnah al-Daa’imah,
25/44 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked
about the ruling on delaying prayer until the time for it is over because of
work, such as a doctor who is on call. 

He replied: Delaying prayer until the time for it is over
because of work is haraam and is not permissible, because Allah says
(interpretation of the meaning): “Verily, As‑Salaah (the prayer) is
enjoined on the believers at fixed hours” [al-Nisa’ 4:103]. And the
Prophet (blessings and peace of Allah be upon him) defined the set times for
prayer. So whoever delays the prayer until after these times or does it
before these times has transgressed the limits set by Allah, and those who
transgress the limits set by Allah are the wrongdoers. So it is not
permissible for a person to delay the prayer until the time for it is over
for any kind of work. But if the prayer is one that may be put together with
the one that comes before it or after it, and it is difficult for him to
offer each prayer at its own time, then he may put the prayers together,
such as if his shift at work is during the time for Zuhr, and it is too
difficult for him to pray Zuhr on time, then he may put it together with
‘Asr prayer, and by the same token he could put ‘Isha’ prayer together with
Maghrib, because it is proven in Saheeh Muslim that Ibn ‘Abbaas (may
Allah be pleased with him) said: The Messenger of Allah (blessings and peace
of Allah be upon him) put Zuhr and ‘Asr, and Maghrib and ‘Isha’, together in
Madeenah when there was no state of fear or rain. They asked Ibn ‘Abbaas:
What was the purpose behind that? He said: He did not want to make things
difficult for his ummah — i.e., he wanted to avoid making things difficult
for them by not putting prayers together. End quote from Majmoo‘ Fataawa
Ibn ‘Uthaymeen (12/33). 

And Allah knows best.