Giving salaams to people in the mosque during the khutbah
Question

                Is it the sunnah to say assalaamu 'alaykum
      out loud when entering the masjid (while others are praying or during the khutbah) ?
      Please advise the daleel. Jazzakallhu Khayrun
Praise be to Allah.The author of Zaad al-Mustanfi said it is
    permissible for the imaam to greet the congregation with salaam when he faces them. Shaykh
    Ibn Uthaymeen said, in his interesting comment, that this is because this practice
    was reported from the Prophet 
 (peace and blessings of Allaah be upon him). Even
    though there is some weakness in this hadeeth (i.e. in its isnaad), this is what the ummah
    has done and it is well known that when the imaam comes and gets up on the minbar, he
    greets the people with salaam. (Reported by al-Shubi). Abu Bakr and Umar used
    to do this. Reported by Abd al-Razzaaq , Ibn Abi Shaybah, 2/114, Ibn Maajah and
    al-Tabaraani. It was also reported by al-Bayhaqi from Jaabir ibn Umar, narrating
    from the Prophet 
 (peace and blessings of Allaah be upon him), then he said: a report
    concerning this was narrated from Ibn Abbaas from Umar ibn Abd
    al-Azeez. Then the shaykh said in his commentary: it is not permitted to speak when
    the imaam is delivering the khutbah, it is only permitted before and after the khutbah,
    even after the khateeb has arrived and after the adhaan, so long as the khateeb has not
    started his khutbah. (Ibn Uthaymeen, Al-Sharh al-Muttabi li Zaad
    al-Mustanfi, 5/78). [?? Makath ??] is well known, from which we know that it is
    obligatory to return the greeting of salaam, so in this case we understand that it is not
    forbidden to speak. And Allaah knows best. 
    Ibn Qudaamah said in al-Mughni: When the imaam faces the
    people, he greets them with salaam and they respond, then he sits down. Then he
    mentioned the hadeeth quoted above, and others. Then he said (may Allaah have mercy on
    him): When he greets them with salaam, the people should respond, because it is more
    of an obligation to return the greeting than to initiate it. Then he should sit down and
    rest until the muadhdhinoon (muezzins) finish. (al-Mughni 2/297). And
    Allaah knows best. May Allaah bless our Prophet Muhammad and his family.