Do Muslims pray like Christians should?

No everyone prays however they wish to pray to the Lord. You don't need anyone to tell you how to pray.

I add citations since my post was taken down.(copied from previous post)

Moses bowed low in reverence, and so did many others, but he also prayed with arms outstretched. (Exodus 9:27)

Abraham fell upon his face (Genesis 17:3).

Solomon prayed kneeling (1 Kings 8:54)

Jesus prayed looking up to heaven (Mark 6:41)

Others prayed with head bowed. (Genesis: 24:26)

They prayed differently at times so pray how you want to

A person can pray whereever and however they want. However, there are times and seasons and reasons for particular postures for prayer within Christianity.

“Woman,” Jesus replied, “believe me, a time is coming when you will worship the Father neither on this mountain nor in Jerusalem. You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews. Yet a time is coming and has now come when the true worshipers will worship the Father in the Spirit and in truth, for they are the kind of worshipers the Father seeks. God is spirit, and his worshipers must worship in the Spirit and in truth.”

John 4:21-24 NIV

The important thing is that we worship God in spirit and truth

However:

https://www.dailymail.co.uk/news/article-6940493/Pope-Francis-lays-floor-pray-middle-St-Peters-Basilica-Good-Friday-service.html

The Good Friday Mass is the only time I've ever seen anyone pray face down. Never heard that it has anything to do with Nehemiah, but I wouldn't put it past the liturgists, they work in the Bible all over the place without people noticing.

No. Public displays of prayer are something Jesus instructed against.

When Jesus's disciples asked Him how to pray, he responded as follows:

And when you pray, do not be like the hypocrites, for they love to pray in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full. But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you. And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words. Do not be like them, for your Father knows what you need before you ask him.

“This, then, is how you should pray:

“‘Our Father in heaven, hallowed be your name,

your kingdom come, your will be done, on earth as it is in heaven.

Give us today our daily bread.

And forgive us our debts, as we also have forgiven our debtors.

And lead us not into temptation, but deliver us from the evil one.'"

For if you forgive other people when they sin against you, your heavenly Father will also forgive you. But if you do not forgive others their sins, your Father will not forgive your sins.

Matthew 6:5-15

From this, we can see that the public displays of submissive prayer, as it is practiced by Muslims, are something that Jesus warns against.

However, he doesn't speak about the proper posture of the body during prayer, so I don't think it matters. If it helps you attain the proper state of mind, it's fine. You can bow face first on the floor of your room like Muslims do if you wish, but you can also just nod your head and close your eyes while clasping your hands like many Christians do, or look up to the sky and spread out your hands like many Pentecostal Christians do.

Nehemiah's posture is only one of many recorded in the Bible.

Among the others:

• Moses bowed low in reverence, and so did many others, but he also prayed with arms outstretched. (Exodus 9:27)

• Abraham fell upon his face (Genesis 17:3).

• Solomon prayed kneeling (1 Kings 8:54)

• Jesus prayed looking up to heaven (Mark 6:41)

• Others prayed with head bowed. (Genesis: 24:26)

• Paul commanded people to pray "lifting up holy hands" (1 Timothy 2:8)

Given the variety of postures used and commanded, there is clearly not a posture of prayer that is the only correct one.

Jesus also cautioned against ostentatious prayer.