Does a person get my replies on Twitter?

[Shannon]

I sent this girl a reply to her post. She is not following me but I am following her. The reply only shows up on my homepage but it does not show up on hers. Did she get the reply? How do you know? I'd also like to send a direct message but she's not folowing me! I tried to reply to her to get to follow me but she won't reply. I don't think she got the reply! Do they send you an email? BEcause once I replied and they replied back but I didn't get an email? How does this work? please explain well. Thanks so much!