Thank you so much for correcting this. I am a super beginner, learning hiragana at this moment so my words and grammatically structure are very limited, hopefully will improve in time.

1) Regarding the first sentence, how would you write in Japanese - "this is my friend's rabbit?"

I’m so sorry for my unkind corrections.
I’ll try to answer your question, but for my poor English skills, there might be some difficulties to express what I want to say.
Please forgive me.

1) The sentence, “This is my friend’s rabbit” can be translated into
これは私の友達のうさぎです。
This is grammatically correct.

2) But, this sentence has two meanings.
1: This is the rabbit that my friend has.
2: This is the rabbit that is my friend.

3) You wanted to write in the later meaning. Is it right?

4) So, if I translate the sentence “ This is my friend’s rabbit “ into Japanese,
I’ll write like this to clarify the meaning:
これは友達が飼(か)っているうさぎです。

I hope this explanation can make senses ….
Although I made a correction about it, I think you did your best!
I enjoyed your lovely sentence.

Thank you sooooo much. It makes much sense now.

No prob! I am relieved!