Yes they are; however, on numbers one through five, the "the" should not be there.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
All these are suitable in a formal letter:
Awaiting your reply.
Waiting for a reply.
Waiting for your reply.
Looking forward to hear from you.
I look forward to hearing from you.
Awaiting your response/feed back/comments.
Prajwal
Several of the choices mentioned earlier are only phrases. My advice is to use only full sentences in a formal letter.
Clive
Looking forward to your reply. This is just a phrase.
I am looking forward to your reply. This is a full sentence, better for a formal letter.
Clive