Are there any differences between useing For or To in some situations like these?
For improvingyour writing, you have to read book more.
To improveyour writing, you have to read book more.
I killed that person
to protectyou.I killed that person
for protectingyou.
In your first example, no. It's just a stylistic choice. 'Improving' is a good choice in your first example because the nicely conveys ongoing improvement.
In your second example though, it's a complete disaster. You've changed the meaning entirely. "I killed that person for protecting you" sounds like the first person killed someone for the reason that they protected the second person.
