返事 and 返信: answering and replying to messages
Distinguish responses to speech or a call from replies sent to received messages.
The broader word for a response
返事 is read へんじ and refers to a response to a question, request, or call. 「名前を呼ばれたら返事をしてください」 asks someone to answer when their name is called.
「誘いの返事を待っています」 means waiting for a response to an invitation. 返事 itself does not indicate whether the answer is acceptance or refusal.
Sending a reply to a message
返信 is read へんしん and means sending a reply to an email, letter, or message. 「メールに返信しました」 means that the speaker replied to the email.
「返信は不要です」 says that no reply is needed. It is neither a ban on reading the message nor a statement that a reply has already been received.
Overlap and limits on substitution
For email, both 「メールの返事」 and 「メールへの返信」 are possible. 返事 broadly covers the response and its content, while 返信 makes the return-message relationship explicit.
Saying 「はい」 when your name is called in class is normally 返事. It is not a reply sent to a received piece of writing, so 返信 is not a substitute here.
Does 「まだ返信していません」 mean that the speaker has not received a reply?
Show the answer and why
No. It means 'I have not replied yet.' To say that the other person's reply has not arrived, you can use 「まだ返信が来ていません」.