First:
Raising the hands while pronouncing the opening Takbir (saying "Allahu Akbar") at the beginning of prayer (Takbirat Al-Ihram) is a recommended act (Sunnah) according to the Hanafi school and the majority of scholars.
Al-Marghinani (may Allah have mercy on him) said in Al-Hidayah (1/48): "And he raises his hands with the Takbir and it is Sunnah, because the Prophet (peace and blessings of Allah be upon him) consistently maintained it" (Al-Hidayah, 1/48).
Al-Babarti (may Allah have mercy on him) said in Al-`Inayah (1/280): "Raising the hands at the beginning of prayer (Salah) is a Sunnah without disagreement."
Therefore, if the Imam holds the microphone in one hand and raises only the other, it does not harm the prayer. This is because raising the hands is a recommended Sunnah and not mandatory, so omitting it does not invalidate the prayer.
It is better to raise the hand holding the microphone as well. This is especially important according to the opinion that one should raise the hands first, then make the Takbir (saying Allahu Akbar). The same applies to the view of doing both actions simultaneously, as this is also possible.
It was said in Al-Hidayah in the previous reference: "What is narrated from At-Tahawi (may Allah have mercy on him), and what is more correct: is that he raises his hands first, then says the Takbir." (End quote)
Second: The Hanafi school held that actions invalidate the prayer if they are excessive.
It was stated in Maraqi Al-Falah, p.120: "Excessive actions invalidate it, not minor ones. The distinction between them is that excessive actions are those where an observer of the doer would not doubt that he is not in prayer, and if there is doubt, then it is considered minor according to the most correct opinion."
Another explanation states that three consecutive movements are considered excessive, while anything less is considered minimal. (End quote)
At-Tahtawi said in his commentary on it: "Ibn Amir Hajj said: The term 'observer' refers to someone who has no knowledge that the person is in prayer." (Hashiyat At-Tahtawi).
Regarding the definition of excessive action, Az-Zayla`i (may Allah have mercy on him) said in Tabyin Al-Haqa'iq (1/164): "It is disliked to fan oneself with a fan or with one's sleeve. This does not invalidate the prayer unless it becomes excessive, as minor actions do not invalidate prayer by consensus, while excessive actions do. They differed about the distinction between them, and there are five opinions:
The first: Actions typically performed with both hands are considered excessive - even if done with one hand - such as wearing a turban, putting on a shirt, tightening trousers, and shooting from a bow. Actions typically performed with one hand are considered minor even if done with both hands, such as removing a shirt, loosening trousers, putting on and taking off a cap, removing a bridle, and similar actions.
The second: Three consecutive actions are considered excessive, while fewer actions are considered minor. For example, if someone fans themselves three consecutive times with a fan, scratches a part of their body, throws three stones, or plucks three hairs, their prayer becomes invalid. However, if these actions are done with intervals, they do not invalidate the prayer even if numerous.
The third: An action is considered excessive if it is intentional, while unintentional actions are considered minor."
The furth: The matter is delegated to the judgment of the one affected by it, who is the person praying. If he considers it much, then it is much, and if he considers it little, then it is little. This is closest to Abu Hanifah's (may Allah have mercy on him) approach. It is his way not to estimate in such matters, but to delegate it to the judgment of the one affected by it.
The fifth: If an observer looks at him from afar and has no doubt that he is not in prayer, then it is much and invalidates the prayer. However, if there is doubt, then it does not invalidate it, and this is the most correct opinion. (End quote)
If the Imam continues the prayer (Salah) while holding the microphone in his hand, with his other hand under his navel, this is considered a minor action that does not invalidate the prayer. This is because an observer would not be certain that he is not in prayer. Similarly, if he does not place his left hand under his navel, the most an observer might do is doubt whether he is in prayer, and this does not invalidate it.
The Imam should not let holding the microphone prevent him from performing the Sunnah acts, such as grasping the left hand during standing, placing the hand, even partially, on the knee during Ruku` (bowing. It should also not prevent him from the obligation of placing the hand on the ground during Sujud (prostration). Placing both hands on the ground during prostration is Sunnah according to the Hanafi school.
Az-Zayla`i (may Allah have mercy on him) said: "He said (may Allah have mercy on him): (And placing his hands and knees), meaning placing them on the ground during prostration, due to the Prophet (peace and blessings of Allah be upon him) saying: 'I have been ordered to prostrate on seven bones' (Narrated by Al-Bukhari and Muslim) and he counted among them the hands and knees. This is Sunnah according to us because prostration can be achieved without placing them. As for placing the feet, Al-Quduri mentioned that it is obligatory in prostration." (Tabyin Al-Haqa'iq, 1/107)
In Ash-Shalabi's footnote on it: "Al-Kamal said: As for making the placement of feet obligatory, it is because prostration while raising them resembles playing more than glorification and reverence, and placing one toe is sufficient." (End quote)
Placing part of the hand during Sujud (prostration) is sufficient.
If he puts one microphone in front of him while standing and another on the ground, which is common in many mosques, this would be better for him. It would eliminate the need to hold and move the microphone during Salah (prayer).
And Allah knows best.
