Who First?

Hadith - Sahih Bukhari 8.251, Narrated Abu Hurayrah
Allah's Apostle said, " The riding one should greet the walking one,
and thewalking one should greet the sitting one, andthe small number
of persons should greet the large number of persons. "
Hadith - Malik's Muwatta Book 53, Number 53.1.1
Yahya related to me fromMalik from Zayd ibn Aslam that the Messengerof
Allah, said," The one riding greets the one walking, and when one of a
group of people gives a greeting, it is enough for all of them. "
The person coming or going, should first offer the salutation (salaams):
Hadith - Abu Dawood 5189, Narrated Abu Hurayrah
The Prophet said: When one of you comes to an assembly, heshould give
a salutation and if he feels inclined toget up, he should give a
salutation, for the formeris not more of a duty than the latter.
The pious muslims is anxious to give salaams first
Hadith - Abu Dawood 5178, Narrated Abu Umamah
The Prophet said: Those who are nearest to Allah are they who are
first to give a salutation.
During Salah
Hadith - Al-Tirmidhi #991,Narrated Abdullah ibn Umar , Transmitted by Tirmidhi.
I asked Bilal: How did Allah's Apostle respond to them as they greeted
himwhile he was in prayer? Thereupon he said: He only made a gesture
withhis hands (in order to respond to the greeting).
Hadith - Sunan of Abu Dawood 927, Narrated Abdullah ibn Umar
The Apostle of Allah went to Qubato offer prayer. Then the Ansar (the
Helpers) came to him and gave him a salutation while he was engaged in
prayer. I asked Bilal: How did you find the Apostle of Allah
responding to them when they gave him a salutation while hewas engaged
in prayer. He replied: In this way, and Ja'far ibn Awn demonstrated by
spreading his palm, and keeping its inner side below and its back side
above.
Hadith - Abu Dawood 924, Narrated Abdullah ibn Mas'ud
We used to salute during prayer and talk about our needs. I came to
the Apostle of Allah and found him praying. I saluted him, but he did
not respond to me. I recalled what happened to me in the past and in
the present. When the Apostle of Allah finished his prayer, he said to
me: Allah, the Almighty, creates new command asHe wishes, and Allah,
the Exalted, has sent a fresh command that you must not talk during
prayer. He then returned my salutation.
Hadith - Bukhari and Muslim
Ibn Mas'ud reports: "We used to greet the Messenger of Allah while he
was in salah and he would respond to our greeting. When we returned
from Abyssinia, we greeted him [during prayer] but he did not respond
to our salutation. We said to him: 'O Messenger of Allah, we used to
greet you while you were in salah and you used to respond to us!' He
then said: ' Prayer demands one's complete attention.' "