1a] What should be said when the imam sits down between the two khutbahs at Jumu’ah prayer?

Key word - {*Friday Prayers:-}
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1a]
The same may also be said of the imam; he should say du'aa' between
the two khutbahs but it should be silent, asking for whatever he wants
of things in this world and inthe Hereafter.
The same may also be said concerning prostration during Jumu'ah
prayer, after reciting the adhkaar that were narrated from the Prophet
(peace and blessings of Allaah be upon him), one may say du'aa' as one
wishes.
And after the tashahhud and before the salaam, one may say du'aa' for
whatever one wants, aftersaying du'aa' for that which it is narrated
one should say du'aa' for. End quote.
He also said (may Allaah have mercy on him):
Du'aa' during this time is good and is mustahabb, because this time is
a time when it is hoped prayers will be answered. The Prophet (peace
and blessings of Allaah be upon him) told us that on Friday there is a
time when no Muslim slave asks Allaah for something when he is
standing and praying but He will answer him.
The time of prayer is the most likely to be the time when du'aa's are
answered, because of the report narrated by Muslimfrom Abu Moosa
al-Ash'ari(may Allaah be pleased with him), according to which the
Prophet (peace and blessings of Allaah be upon him) said: "It is
between the time when the imam comes out until the prayer ends."
Based on this, one should make the most of this opportunity and say
du'aa' between the two khutbahs.
With regard to raising thehands, I do not think there is anything
wrong with it, because the basic principle with regard to du'aa' is
that its etiquette includes raising the hands.So if a person raises
his hands there is nothing wrong with it, and if he says du'aa'
without raising his hands there is nothing wrong with it. This has to
do with du'aa' between the two khutbahs. End quote.
Fataawa Noor 'ala al-Darb(Fataawa al-Salaah/Salaat al-Jumu'ah)
Thirdly:
Some fuqaha' said that it is mustahabb to recite Qur'aan when the imam
sits down between the two khutbahs, and some of them mentioned Soorat
al-Ikhlaas in particular, based on the hadeeth of Jaabir ibn Samurah
(may Allaah be pleased with him) who said: The Prophet (peace and
blessings of Allaah be upon him) used to give two khutbahs, sitting in
between them. He would recite Qur'aan and remindthe people. Narrated
by Muslim (862). A similar version was narrated by Ibn Hibbaan in his
Saheeh (7/42), which he included in a chapter entitled "Mention of
what the Prophet (peace and blessings of Allaah be upon him) used to
say when he sat down between the two khutbahs." End quote.
Al-Khateeb al-Sharbeeni (may Allaah have mercy on him) said:
His sitting between the two khutbahs was about the length of Soorat al-Ikhlaas.
Should he recite Qur'aan or dhikr therein, or remain silent?
They did not discuss it, but in Saheeh Ibn Hibbaanit says that the
Prophet (peace and blessings of Allaah be upon him) used to recite
Qur'aan therein. End quote.
Mughni al-Muhtaaj (1/557).
The correct view is that the words of Jaabir ibn Samurah in the
hadeeth, "he would recite Qur'aan and remind the people" do not refer
to the sitting between the two khutbahs, rather they refer to what is
mentioned at the beginning of the hadeeth,"The Prophet (peace and
blessings of Allaah be upon him) used to give two khutbahs", i.e., he
(peace and blessings of Allaah be upon him) would deliver two khutbahs
on the minbar, which both included recitation of Qur'aan and
exhortation and reminders to the people.
Hence al-Haafiz al-Dhahabi said in Siyar A'laam al-Nubala' (16/102),
in his biographyof Ibn Hibbaan, in an important discussion of mistakes
made by Ibn Hibbaan in his Saheeh: One of the things which al-Dhahabi
regarded as a mistake on his part was his categorizing of this
hadeeth, when he – Ibn Hibbaan – said: Mention of what [the Prophet]
(peace and blessings of Allaah be upon him) used to recite when he sat
down between the two khutbahs. And he did not mention anything. End
quote. Meaning that the hadeeth does not indicatewhat he mentioned in
thechapter heading.
The more correct view –and Allaah knows best – is that there is no
binding Sunnah from the Prophet (peace and blessings of Allaah be upon
him) concerning this matter. The one who wants to use this brief
moment of silence to say du'aa' or dhikr or recite Qur'aan may do so,
so long as he does not disturb others.
And Allaah knows best.