Learn English – Are there better ways to say “I like the sentence someone said” or “I love this sentence someone said”

You could say this:

I'm sorry I can't hear you. You're breaking up!

From Macmillan Dictionary:

break up
5 [intransitive] if the sound on a radio or mobile phone breaks up, you can no longer hear the person who is speaking on it.
I can't hear you, you're breaking up.

There is no unique term, e.g. from psychology, for feelings like that. There are a few for feelings of unification with the world or entire universe and all creatures in it, but not for deep feelings of closeness and identification with one person or one place. The best you can do is describe the feeling.

Use relationship and/or emotional terms:

"She's like a sister to me".

"My friend's mum is so nice that I feel (like / as though) she's my mother too"

"I love Minneapolis. It's as though I've lived here all my life"