Learn English – “Please Find Attached or “Please Find Enclosed” in a formal email

It depends on the situation, of course. Some folks get swamped with email, contending with more than 40 or 50 messages in a single day. If the recipient is a busy person, sometimes it's best not to clutter their inbox.

If the situation warrants an acknowledgment, however, yours is fine, although I might suggest:

Thank you for replying so promptly.

This is minor and subtle, but I think my version is thanking the person for their promptness, while yours is thanking them for their reply. They already know they've replied, so I think my wording has a little more value to the recipient – but that's a debatable point, given that the wordings are so similar.

No, saying "at your convenience" is generally understood to be a polite way of saying that you recognize that the other person is very busy, and so asking them to choose a time for a meeting instead of you selecting a time.

Like almost any statement, a polite statement can be made rude by the context, or if spoken, by the tone of voice. Like if you said, "Well, given that you've failed to show up for the last four appointments we schedule despite your promise that you will attend, and as you apparently have no regard for the time of other people, perhaps you could let me know when you would like to meet, at your convenience", well, that would be deliberately rude. But a simple, "I would like to get together with you to discuss this. Please select a time at your convenience and let me know when we can meet" or something to that effect would be considered very polite.