In the dry heat atin the valley, Clara was planning to her escape. In the dry heat in the valley, Clara was planning her escape.

In the dry heat atin/of the valley, Clara was planning to her escape. In the dry heat in/of the valley, Clara was planning her escape.

In the dry heat atof the valley, Clara was planning to her escape. In the dry heat of the valley, Clara was planning her escape.

The camp chef was using moist heat for cooking, the steam escalating as a sign to the sky, but Clara was not hungry for food, but for; she wanted freedom. The camp chef was using heat for cooking, the steam escalating to the sky, but Clara was not hungry for food; she wanted freedom.

The camp chef was using moist heat for cooking, and the steam escalating as a sign to the sky,going up to the sky like a signal but Clara was not hungry for food, butonly for freedom. The camp chef was using moist heat for cooking, and the steam going up to the sky like a signal but Clara was not hungry for food, only for freedom.

The camp chef was using moist heatfuel for cooking, the steam escalatmoke rising as a sign into the sky, but Clara was not hungry for food, but for freedom. The camp chef was using moist fuel for cooking, the smoke rising as a sign into the sky, but Clara was not hungry for food, but for freedom.

Heat can't be moist, so perhaps you meant "moist fuel"? If you were looking to describe the weather condition, "humid heat" would be the phrase to use, though here, in the context of cooking, I don't see its relevance. Next, steam is invisible and cannot be seen, so I think smoke was what you had in mind. Also, it is not clear what the rising smoke is supposed to be signalling, so allow me to suggest an alternative: "the smoke rising into the sky as a sign that lunch/dinner was ready".

Klara studies alld his routine for days, watches and waits. Klara studied his routine for days.

Klara studies all his routine for days, and she watchesd and waitsed. Klara studies his routine for days and she watched and waited.

KClara studies alld his routine for days, watchesing and waitsing. Clara studied his routine for days, watching and waiting.

The guard was deceitful and manipulative, h. He promised her for safety, but lied with a smile. The guard was deceitful and manipulative. He promised her safety, but lied with a smile.

The guard was deceitful and manipulative, he promised her for safe,ty but lied with a smile. The guard was deceitful and manipulative, he promised her safety but lied with a smile.

The guard was deceitful and manipulative,: he promised her for safety, but lied with a smile. The guard was deceitful and manipulative: he promised her safety, but lied with a smile.

The colon indicates that whatever comes next is an explanation of how the guard is deceitful and manipulative.

She chose her movement time whiletime during dinner, so she sneaked out while no one iwas watching. She chose her time during dinner, so she sneaked out while no one was watching.

She chose her movement time whileduring dinner, soand she sneaked out while no one iwas watching. She chose her moment during dinner, and she sneaked out while no one was watching.

She chose her movement time whileto make her move during dinner, so she sneaked out while no one iwas watching. She chose to make her move during dinner, so she sneaked out while no one was watching.

"make her move" is a set phrase which means "to act". Also mind the tense: "is" should be in the past tense ("was").

She had to outsmart him, and she did. She had to outsmart him and she did.

She is now gone amongst the hills, under the desert’s hot sun, eventually free. She is now gone amongst the hills, under the desert’s hot sun, free.

She iwas gone, out among the hills, under the desert’s hot sun, and was eventually free. She was gone, out among the hills, under the desert’s hot sun, and was eventually free.

She iwas gone among the hills, under the hot desert’s hot sun, eventu sun, finally free. She was gone among the hills, under the hot desert sun, finally free.

"desert's hot sun" is fine, but "hot desert sun" sounds much more natural.