Re: telephone conversation
To me, the most obvious answer "May I let him know who's calling?" (or something along those lines) is missing.
Maybe those days are gone, but it used to be that you would inform Mr. Smith who was calling and Mr. Smith could choose to take the call or have you take a message, with a "I'm sorry - I didn't realize Mr. Smith wasn't availble/Mr. Smith is on his other line. May I take a message?" type follow-on.
"Hang on" would piss me off as a caller. "Of course - let me put you through" would be fine but not the "Of course you can."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.