Just three vague sentences

Hi. I need some helps on these sentences. I'm pretty sure of my translations but i just wanna make sure of it.

放課後生物準備室
After School Biology Lab
(準備室 is "preparation room" in jisho. But i thought it sounds better with "lab". Or may be i'm completely wrong?)

もっといろいろ見せてよ
Show me a lot more
(At first i was thinking of putting it "Show me a lot more, won't you?" But that would have been 「もっといろいろ見せてくれるよ」isn't it? So i'd like to ask others opinion on this)

そのドラマ先生蘭�録画してっから
Sensei has already pre-recorded that drama

Thanks!

放課後生物準備室

This one sounds like 放課後 and 生物準備室 got bunched up together intentionally, like　放課後、生物準備室に来てよ (Come to the biology lab after school!) or something like that. The words you've got are correct.

もっといろいろ見せてよ Show me a lot more
You've got it right. "Show me a lot more, won't you?" is also correct as well. 見せてよ is a casual, informal request while もっといろいろ見せてくれるよ is not a question or a request at all.

そのドラマ先生蘭�録画してっから　Sensei has already pre-recorded that drama

As far as I can tell without any context, you've got it right.

...This one sounds like 放課後 and 生物準備室 got bunched up together UNintentionally,

I thought もっといろいろ見せてくれるよ was supposed to be a softer way to ask for something. I guess it's not. Thanks for the heads up.

「放課後生物準備室」 is actually a title. Not a dialogue. So would it be ok to say "After School in the Biology Lab"?

- もっといろいろ見せてくれるよ is simply saying "(Someone) shows me a lot more" or "(Someone) does me the favor of showing more. I think you _might_ be referring to もっといろいろ見せてくれない？ for "Won't you show me more?" or "Won't you do me the favor of showing me more?"

- As a title, then, yes, "After School in the Biology Lab" would be fine for 「放課後生物準備室」. Sorry I had no idea that it could be a title.