1. The pen was a gift from my father.
2. The pen was a gift by my father.
(Can we use 'by' instead of 'from'?)
3. I hope you will like this one.
4. I hope you to like this one.
5. I want you will like this one.
6. I want you to like this one.
(#3 and #6 are right, but #4 and #5 are wrong, right?)
7. I was sorry that I was angry at him.
8. I was sorry to be angry at him.
(Are both the same?)
9. I am sorry that I was angry at him.
10. I am sorry to have been angry at
him. (Are both the same?)
#1... no, gift from is best.
Yes, 3 and 6 are correct.
7 and 8, yes, both are correct, and 9 and 10 can both be used.