Why do Shias prostrate on mud?

Abu Sa'eed used to relate that he had seen the Prophet doing his prostration (Sijdah ) on wet mud, so much so that he could see the stains of mud on his forehead.
Saheeh Bukhari, Part I, p. 104

The Prophet used to rest his forehead on the earth (turba) while prostrating.
Saheeh Bukhari, Part 1, p. 97

The Prophet used to do his prostration on Khumrah (Sijdaghah).
(1) Saheeh Bukhari, Part 2, p. 214 & p.243
(2) Jam'a Tirmizee, p.46
(3) Kanzul Ummal, Part 2, p. 12

The Prophet declared that the best spot for prostration was the earth or a thing that grows from the earth.
Kanz-ul-Ummal Part 4. p. 113

"The Prophet said to his wife Umme Salma, "Please fetch the 'Khamrah' (Sajdaghah) from the mosque." The word Khumrah means a small piece of chatai made from palmleaf on which only the head could be rested when prostrating. lbn-e-Aseer in his Jam'a-ul-Usool has written, "Khumrah is the Sijdagah on which the Shi'as of our time perform their prostration on."

"I maintain that by this tradition it is 'sunnat' to keep a 'sajdagah'. Those who forbid it and call it the way of the 'Rafzees' are wrong. To practice this 'sunnat', I often perform my prostration on a fan made from palmleaf and do not care about the criticism of the ignorant. We are concerned only with the 'sunnat' of the Prophet, no matter whether they call it the way of the 'Rafzees' or 'Kharijees'. Let them rave about it."

Sunni 'Alim
Maulana Vahidul Zamankhan
Anwar-ul-Laghat, Chap. 7, p. 118

Why do Shias pray Noon/Afternoon and Evening/Night prayers together?

It is narrated on the authority of Ibn-e-Abbas (that he said) that the Messenger of Allah said the prayers of Zohr and 'Asr together as also the prayer of Maghrib and 'Isha, although he was neither in a state of fear nor on a journey.
Saheeh Muslim, Vol. I p.264

Ibn-e-Abbas narrates that the Messenger of Allah recited the Zohr & 'Asr prayers together and also said the Maghrib and 'Isha prayers together although he was neither in a state of fear nor was there any other cause e.g. rains. It is related from Wakee' that he asked Ibn-e-Abbas the reason (for the joint prayers). Ibn-e-Abbas replied "So that the followers may not experience inconvenience and difficulty."
(1) Saheeh Muslim, Vol. I, p.265
(2) Jam'a Tirmizee, p. 54

Abdullah Bin Shaqeeq narrates that one day after the 'Asr prayer Ibn-e-Abbas began giving a sermon which was so enduring that the sun set and the stars appeared. People began to shout, "Prayers! Prayers! (as it was time for Maghrib prayers). Ibn-e-Abbas paid no heed to them until someone from Bani Tameem stood up and shouted incessantly, "Prayers! Prayers!" Ibn-e-Abbas then said, "Woe unto you! You wish to teach me the tradition!" He said further, "I have personally seen the Messenger of Allah say the Zohr and 'Asr prayers together and the Maghrib and 'Isha prayers together."
The narrator says, "This statement of Ibn-e-Abbas kept pinching my conscience until I went and asked Abu Huraira about it and he attested what Ibn-e-Abbas had said."
Saheeh Muslim, Vol. 1 p. 265

It is related from Ibn-e-Abbas that the Prophet at one time recited seven raka'ats of prayers and at other time eight rakaats (all at once) i.e. he recited the Maghrib and 'Isha prayers together and Zohr and 'Asr prayers together.
Saheeh Bukhari, Part I, p.72

It is narrated by Ibn-e-Abbas that at Medina, the Prophet used to say two prayers together (Zohr & 'Asr and Maghrib & 'Isha) without there being any fear or rainfall. When asked about the reason for this he said "The Prophet desired that his followers may not suffer inconvenience and therefore the two prayers could be recited together.
Sunan Nasaee, p. 290