It doesn't sound like it's gone any further than the conversations you saw on his phone. Honestly, it sounds like they are friends. Is your boyfriend not allowed to have friends? You need to stop snooping through your boyfriends things. I promise you, if you are doing that, your relationship is not perfect. You need to figure out what the underlying problem is here so you don't do that again because it's a complete breach of trust and privacy on your part. People who snoop are insecure, end of story. Either their partner has acted in ways that contributes to those feelings, by cheating and lying, or people are insecure and are looking for something to go wrong in their relationship and for some reason I will never figure out, they seem to want to find it. You even found messages that should have quelled your fears, when you saw that she said "I know you're seeing someone and understand, but we get along well..." that should be a huge sign that your boyfriend is faithful to you and hasn't done anything inappropriate with this woman, but you still think something is up. So either you don't trust your boyfriend and you never truly will, or he's done something to break your trust and you're looking for more evidence.
Do not snoop through your boyfriend's social media accounts, email, or cell phone. It only brings trouble.
"Caring is not an advantage."