Is there singing in Muslim church? If so, I'd like to hear it.
No, a mosque has no singing and no musical instruments. What you heard in the video, is not singing. It is the Qur'an being beautified with the reciter's voice. Muslims try to beautify their voices when reciting. There are rules as to how each letter is pronounced, which part of the mouth/throat is used for that letter, how long to pause on it, how long to stress it, and how much to elongate it, how to join it to the next letter etc. Very often the stresses/ emphasis and elongations, correspond to the meanings of what is being recited in an amazing way. So no recitation sounds nice randomly or as a result of chance. It doesn't have notes etc. However we do not sing the Qur'an and reduce it to the level of a song. If it was sung, like a song, it would be impossible to adhere to the rules of recitation. It may sound the same as as song to you, but there is a difference.
The Qur'an is recited during the five daily prayers, which are pre-sunrise, noon-ish, mid afternoon, post sunset, and night time. The lunchtime and afternoon prayers have the Qur'an recited quietly, though you will hear the phrase Allahu Akbar, which extols the greatness of God. The morning and evening prayers have the Qur'an recited loudly/audibly.
You'll both also notice, that a mosque contains no images or statues, not unlike the Biblical ten commandments.
During prayers, Muslims stand in rows, shoulder to shoulder, and bow and prostrate in unison, facing the direction of Sacred Mosque in Makkah.
In the mosque, if you watch a prayer, your girlfriend will notice that the Muslims are praying similar to the way Jesus (peace be upon him) and the previous Biblical Prophets prayed.
Taking off their shoes to pray
Qur'an
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When he came to the Fire, a voice was uttered: O Moses! I am thy Lord, therefore put off thy shoes, for thou art in the sacred valley of Tuwa."-(Holy Qur'an 20:11-12).
Bible
(And God said to Moses), "Draw not nigh hither: put off thy shoes from thy feet, for the place whereon thou standest is holy ground."-(Exodus 3:5, also Acts 7:33).
They make ablution, washing their faces, hands and feet...
Qur'an
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O you who belive! When you rise up to prayer, wash your faces and your hands as far as the elbows, and wipe your heads, and wash your feet to the ankles."-(Holy Qur'an 5:7)
Bible
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And Moses and Aaron and his sons washed their hands and their feet thereat; when they went into the tent of the congregation they washed as the Lord commanded Moses."-(Exodus 40:31-32).
The faithful face the Qiblah (direction of prayer)
Qur'an
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So turn thy face toward the Sacred Mosque, and (O Muslims), wheresoever ye may be, turn your faces toward it."- (Holy Qur'an 2:144).
Bible
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Now when Daniel...went into his house; and his window being open in his chamber towards Jerusalem, he kneeled upon his knees three times a day, and prayed, and thanks before his God, as he did aforetime."-(Daniel 6:10).
Bowing down and prostrating..
Qur'an
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O you who believe! Bow down and prostrate yourselves and serve your Lord, and do good that you may prosper."-(Holy Qur'an 22:77).
Bible
"And he (Jesus) went a little further, and fell on his face, and prayed..."-(Matthew 26:39).
"And Joshua fell on his face to the earth, and did worship..."-(Joshua 5:14).
"And he (Elijah) cast himself down upon the earth, and put his face between his knees."-(1 Kings 18:42).
"And they (Moses and Aaron) fell upon their faces..."-(Numbers 20:6).
"And Abraham fell on his face..."-(Genesis 17:3).
Spreading out their hands to God, asking forgiveness, seeking His blessings, beseeching His protection..
Qur'an
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Our Lord! Give us good in this world and good in the Hereafter, and defend us from the torment of the Fire."-(Holy Qur'an 2:201)
Bible
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...when Solomon had made an end of praying all this prayer and supplication unto the Lord, he arose from before the altar of the Lord, from kneeling on his knees with his hands spread up to heaven."-(1 Kings 8:54)
Muslims around the world, and all the Prophets, including those that came before Muhammad (peace be upon them all) prayed in a similar way. We are merely following in their footsteps.
Peace.