(CNN) At the age of just four, Satabraq finds soldiers and rockets more normal than classrooms and schoolmates.

Satabraq meanders the alleyways in the Old City of Mosul, a place that is both her home and a frontline. Dressed in red floral pajamas, she is led by Iraqi troops who laugh and play with her between firing mortar rounds.

"The first environment she has ever been exposed to is the police. She loves them more than she would students in a school," Abdullah, her father, said. "She plays with them and they bring her sweets."

Satabraq's family is among the estimated 400,000 civilians, about a quarter of Mosul's pre-war population, trapped in the Old City, according to the United Nations.

The densely populated historic center of Iraq's third largest city once bustled with life, but now most streets are quiet, spectral.

"Civilians in Mosul face incredible, terrifying risks," Lise Grande, the UN's humanitarian coordinator for Iraq, said this week.

"They are being shot at, there are artillery barrages, families are running out of supplies, medicines are scarce and water is cut off. Nothing is more important than protecting civilians -- nothing."

Iraqi federal police Hummer firing towards ISIS positions in the Old City of Mosul. #cnn #mosul #isisbattle A post shared by Salma Abdelaziz (@salmaazzizcnn) on Apr 20, 2017 at 12:22pm PDT

Trapped by ISIS

Satabraq's family sits near an Iraqi federal police firing position, making their home an obvious target for ISIS -- a reality that either doesn't bother or doesn't occur to the girl's father.

The alleyway is ringing with the constant cacophony of war. Satabraq's disabled grandfather sits in a wheelchair sporting wrap-around shades, holding an old ice cream tub of his medication and wearing an indifferent expression.

"She was supposed to go to school but she couldn't under ISIS, so she has trouble speaking," Abdullah said. "There was nothing for her, no education, nothing. ISIS came, we shut our doors, and she was never allowed out."

The brutal fight for Mosul

At the center of the Old City's winding streets is al-Nuri Mosque, the ideological heart of ISIS in Iraq.

In 2014, Abu Bakr al-Baghdadi stood on its 12th century pulpit and announced the creation of the so-called Islamic caliphate. It was the first and last time the leader of the terrorist group spoke publicly to his followers.

Now, on the mosque's famed leaning minaret, the black and white ISIS flag still flutters.

The Iraqi federal police, who defend and fight for this area, exclaimed, "Next Friday, God willing, we will pray in al-Nuri."

It is a difficult promise to keep. The police units are losing men daily to ISIS's counter assault. And the frontline, just on the outer edge of the Old City, is so fluid, it's often hard to tell who has the upper hand.

Narrow alleyways make it difficult for Iraqi troops to fight back ISIS in Mosul's Old City. #isisbattle #mosul #isisbattle A post shared by Salma Abdelaziz (@salmaazzizcnn) on Apr 20, 2017 at 12:26pm PDT

At best, Iraq's federal police are engaged in a brutal game of hide and seek, advancing a number of meters at a time, only to risk being pushed back there or elsewhere by extremists.

Each day that troops fail to gain ground, ISIS's mass hostage standoff of civilians trapped inside continues, unabated. Families are herded into kill zones, unwilling cannon fodder as the group desperately tries to cling to control.

"They would besiege us and use (us) as human shields. If you left your house, you would be killed," Raji Abu Fawaz, a Mosul resident, said. "They would call on the mosque loud speaker saying, 'Do not leave your homes.' And some left and were killed."

"ISIS would take people and families... we would see them from our house."

Children who fled the fighting in western Mosul waiting at a collection point for displaced families.

Waiting for relief

Every street, every home bears the scars of the grinding urban warfare. A colonel says the battle could be hastened with precision firepower from the US-led coalition.

"So far the (American) contribution is weak," he said stoically. "The American military has very strong capability. They have advanced and precise weapons, and with their intelligence they can help us. We hope they will help us more."

Many children are among the families who've fled Mosul, with harrowing stories of their treatment by ISIS fighters.

On the outskirts of the city, those lucky enough to have escaped the hell inside sit with bundled belongings, waiting for buses to transport them to safety. But escape from ISIS has not relieved them of fear for loved ones.

"Up until now my brother is besieged and so is the rest of my family. My brother, they came and hit him with sticks and dragged him to another neighborhood. He is crippled and they wouldn't let him go anywhere," Ifsha Mohammed, a Mosul resident who fled, said.

"If they (ISIS) want to take someone, they come to the door with their weapons and threaten them. Either they go with them or they die."