In Japanese script how does it write in: sensei, genki desuka?

Question:

In japanese script how does it write in: sensei, genki desuka? nasurin san ni oboeteimasuka? kore wa, long time no see. sore wa mata ne. take care

Answer:

先生、元気ですか?
NASURINさんを覚えていますか?
これは、久しぶりでした。
それは、またね。
お気をつけて。

First, you might want to reconsider this sentence: "kore wa, long time no see". Especially the "kore wa" part. Also, "mata ne" is kinda casual, so it might not be the best choice of words when speaking with your sensei.
Secondly, I added NASURIN because there is no way for me to know how she would write her name. I would guess ナスリン in katakana but, really, this depends on the person itself.

EDIT: Rotbuche is of course right; kinda skipped over it as I was only really paying attention to rewriting it. (Corrected it meanwhile)
Also, he gave a correct answer about "I miss you as well", though, taking in consideration the wording of the prior sentences I would rather take "kimi". (more familiar, casual).
君がいなくて寂しい。
Also, he interpreted Jane as a name, which could be true, but if you happened to mean "Ja/Jaa ne" as in "bye/later" then it is: じゃね。