1. I suppose you solved that issue. - perfect
2. Scientists casually discovered a dinosaur's bones. - "Casually" sounds strange. It sounds like they don't care, but what you mean, I assume, is that it was an accident/not planned. Try "Scientists accidentally found a dinosaur's bones".
3. He is addicted to music. He imagines melodies from time to time. - perfect.
4. She is afraid of hooking worms for fishing. - perfect
5. I hope they solved how to overcome the obstacle. - perfect.
6. Look! We almost approach the castle. This is a sound building, isn't it? - The verb "approach" is strange with "almost" before it. They can see the building already, so they ARE approaching. "Look! We are approaching the castle" is better. I do not know what you mean by a "sound" building??
7. I always envy somebody. It is one of my shortcomings. - perfect.
8. Grandmother's cognitive process resembles her 5-year-old grandchild. - you need to use "The" at the beginning, and rephrase a little too.
"The grandmother's cognitive process resembles that of her 5-year-old grandchild".
9. He has deprived her of money. It seemed ideal marriage, but it cracked. - It seemed AN ideal marriage.
10. I hated olive when I was a child, they had a distinctive taste. 2 things - you need to use the plural "olives". Also, using "had" suggests that they now do NOT have a distinctive taste.
I would say: "I hated olives when I was a child. They have a distinctive taste".