1. "I want you to present about 5 of your definitions in your self-made dictionary to the class, then I will ask you about 4 or 5 other specific letters and what you found. "
I've never seen "letters" used as a substitute for "words" and I suspect this is a mistake.
2. Is there a better way to say "Please handle it (the self-made dictionary) with gentleness, because it may easily fall apart"?
Though there is nothing actually incorrect with this, the use of "gentleness" in this context is unusual. More usual would be "care", i.e.
"Please handle it (the self-made dictionary) with care, because it may easily fall apart"
Student or Learner