Answer:
I don't know to whom you think you're speaking like that.
Step-by-step explanation:
To put it simply, if you can answer this with "her" or "him", then use whom. If you can answer this with "he" or "she", use who.
"I don't know to whom you think you're speaking like that."
"I'm speaking to HIM."
Being able to answer it with him means that the proper usage of whom is in this sentence.
FURTHERMORE, you can use this to disprove the other sentences.
"I wonder whom is at the door this late at night."
"She is at the door." You would use who in the sentence, not whom.
"To who are you mailing all those thank you notes to?"
"Him." You would use whom in this sentence, not who.
"Who are you texting to all day and all night?"
"Him." You would use whom in this sentence, not who.