A. My phone is broken. Can I use your phone? OK Sentence but use "May I use your phone".
B. Sure, come on in. OK Sentence
A. Thank you for letting me in. OK Sentence, but It sounds creepy.
A lot of people wouldn't do that or Most people wouldn't do that. NOT REALLY CORRECT. Use "this" instead of that.
B I don't usually. OK Sentence.
When you say "thank you for letting me in" to me it souds a little creepy.
Instead, say something like, "thank you for helping me out" Not too many people would do THIS. You would not use "that" because what you are asking is something happening now.
Here would be my dialogue. Let me just add something. When you are asking a favor from someone, you better be as polite and informative as you can. My example:
Hi, my name is John. I live down the hall (or whatever. Let them know who you are).
I'm so sorry to bother you but my phone isn't working. May I use yours? It's a local call. I need someone to pick me up and I have to call him. (or whatever the reason may be. Be informative)
Sure, come on in.
Thank you so much. I know, not too many people would do THIS. You're very kind.
I usually don't.