Whose phone was connected to the microwave? Who did her message reach to change it, and if she kept it a secret, how did they know whose phone to use on the microwave? Am I forgetting/missing something?
The mistake you're making is that the phone attached to the microwave is irrelevant—any phone is okay.
The phone that matters is the phone that the microwave phone sends the message to.
The message is sent to Faris's father, Yukitaka Akiha.
The reason could be classed as spoilers, so make sure you watch the show first.
Yukitaka died in a plane crash several years before the events of Steins;Gate. He was the only victim of the crash. However, his daughter later uses a D-Mail to save his life, by making him believe she was kidnapped and forcing him to take the bullet train instead.
Her message was sent back in time to her father's phone. The message she sent changed the fact that he had gotten on the plane and died. Without her father in the picture, she sparked the existence of the moe culture in the city. But with her father in the equation, she had never sparked the moe‑ization of the city.
Here's a quote from the Steins Gate wiki regarding the message sent back:
She joined in episode 9, recruited by Rintarou because she wanted to make a D-Mail to avoid her father's death.
I believe it ended up taking out May Queen (the cafe) and replaced it with some other store. The Akiba district was also heavily influenced by the D-Mail.
Answering your question of who sent it, I believe Faris sent it herself.
Here's a discussion on the episode that you might want to check out as well.