That's what I make of it: You have addressed the teacher as "du" in writing, you probably did it for the first time, and the teacher could either reject this too personal and friendly approach or accept it. By saying "sagen wir du", properly, "sagen wir 'du' zueinander", she accepted it: okay, let's communicate on this personal level. She goes on to use "du" in her mail. I assume that you are not a 15-year-old at school but a grown-up student. This would change my interpretation of your teacher's reply, so if I'm mistaken, please make this clear. I guess that you're a college student and older than 18.
In German, the "default value" for talking to each other among grown-ups is "Sie". This is particularly true when hierarchies are involved auch as between boss and employee, teacher and student. This distinction between a formal and respectful form of address and a personal level among friends is present in many languages, French or Spanish among them, but is not observed in English, where "you" is the uniform way of addressing each other.
In languages in which a formal and a personal way of addressing each other exist it is usually up to the older person or the person higher in hierarchy to decide if communications should be continued on a more friendly level.
In this case, it seems, you have addressed your teacher in the "du"-mode without having been offered this "step-down-in-formality". Apparently, she didn't take offence. Probably recognizing that your approach was not a conscious attempt at establishing a familiarity that was not per se warranted by your relationship, she chose the more relaxed approach of accepting your "du" and addressing you as "du" as well. But she had to reserve her right, as the one higher in hierarchy, to accept or reject your proposal. That's why she started her mail with "Sagen wir du". It means: Let's determine the level of our communications. You're a student and I would have expected you to address me as "Sie". You call me "du" in what you write, and I don't take exception to it, so let's stick to this (because I like you and would like to be friends with you, or, simply, because I can't get these subtleties into your heads).
Does this make it any clearer?
P.S.: Yes, there are errors in your letter, but they sound charming. It's perfectly clear what you mean even if there are some hazards of German grammar you couldn't successfully avoid.