1) I think you should say 'comments', as the box was made to contain comments. 

And I'm afraid it does sound a little odd. What I think you're trying to say might be written like this: "Talking Tuesdays Quiz Night opens tonight!". Unless I've misinterpreted what you've written, you wouldn't put an apostrophe in Tuesdays either, as the 's implies that Tuesday owns the quiz. 

2) I might need a little more context to be sure, but I'd interpret "do well" in one of two ways:

    a)  'Earth individuals would do well to meditate... etc.' meaning that it is something that would be good for them

    b)  'Earth individuals are good at or have some kind of natural ability to meditate... etc.'. 

Hope this helps! 

Hi Natalia. Here's what I would write:

"Please remember that you have the tutorials are there to help you. Make sure to check the provided material for your answer before coming to me. Do not turn to me with a question before searching if the answer is in the material I already sent you. It is important that I recommend you keep them in a handy place in on your computer, since as you will need to check them frequently at the beginning." 

Hope that helps. I'm no tutor or teacher, but I think it reads a little better now. 

Buena suerte