Hey, welcome back! I agree with your translations
(For sentence 1, I would rather go with “It looked like that she was showing off to Kiki”… But your version definitely captures the gist.)
For the last sentence, it is broken down like this, I think:
あたしからの贈りものだ - it is my present
って - quotation (と言う)
いわないでほしいの - I want you not to say
It’s maybe only a nuance, but the nominalizer does not carry no information at all It’s like the difference between “to do” and “the doing”, so to speak, so it emphasizes the concept of the action instad of the action itself. It sometimes helps me to rephrase it with “the fact that…”.