1. I thirst and going to swallow a whole bucket of water.
--->I am thirsty, I can drink a whole bucket of water.
2. He is addicted to her, maybe because she has a pretty dimples on her cheeks.
-->He is addicted to her ( in love with her/ attracted to her??) may be because she has pretty/cute dimples on her cheeks./ may be because of her cute dimples.
3. There was a false route, hence they got lost in the woods.
--> It was the wrong route, hence they got lost in the woods.
4. I casually knew, that she wear lens, apparently she hesitates to wear glasses.
--> I knew that she wear lenses, apparently she hesitates to wear glasses.
5. He insulted Ann. This circumstance revealed his real temper. He is not gentle in general.
--> He insulted Ann, these circumstances revealed his real nature/temper. He is not gentle in general.
6. He has a bad habit to boast his rewards.
--> He has a bad habit of boasting about his achievements.
7. The tiger's offspring rely on their mother.
--> The tiger's offspring/cubs rely on their mother.
8. He feel remorse when he casually insult his colleagues.
--> He feels remorse that he unintentionally/unknowingly insulted his colleagues.
9. The offspring of lion are very cute creatures.
--> The offspring/cubs of lion are very cute/ very cute creatures.
10. The wheel rotates around its axis.
--> The wheel rotates about it's axis.
I hope that helps. Some of the sentences might have been correct but i changed anyway.
Just a suggestion, don't give more than 2 or 3 sentences in one question, it will be easier to answer and you will get more replies.