"I have not received a response from Mary to my letter." or
"I have not received a response from Mary to the letter I sent to her a month ago."
 There's no need for "number" here.
 "many times in the past few weeks." If it's more than a few weeks, you would tend to say the exact number instead. So, "many times in the past 6 weeks."
 "there has been no-one picking up the phone." There is no need for the not, because you've already created the negative form by using no-one.
Also, you can use pick up the phone, answer the call or answer the phone, but not pick up the call.
I have not received a response from Mary to the letter I sent to her a month ago. I have called her telephone many times in the past few weeks but that number keeps ringing and there has been noone picking up the phone. I believe Mary has moved to a new address.
Pretty good all around.
- For Teachers