Learn English – “Will you close the door” vs “Could you close the door”

There is absolutely no difference between them with regard to politeness. English is just not that sensitive to politeness: we don't have the finely-striated levels of politeness of, say, Japanese. Context and tone of voice can change any of them from a very polite request to a direct order with a veneer of politeness.

There is a slight difference in meaning, or at least emphasis. "Can you please do this" emphasizes the request, while "Can you do this please" emphasizes the task: the former asks you to do something, but what that something is is not that important. The latter asks you to do this, not that. However, this difference is very, very slight. And again, context and tone of voice can drastically change the interpretation.

There's no rule against using the same auxiliary verb, including will, more than once in a sentence.

Consider these two examples, written by native speakers, found in a search for "will decide that he will":

My husband, who is a pediatrician, still holds on to a hope that Adrian, one of our youngest, will decide that he will do it after all.

(source)

and

It may well be that the circumstances are such that the franchisor will decide that he will terminate the contract...

(source)

In fact, you could have used it three times by using will before come, but it's probably better to avoid that much repetition.

So there is nothing wrong with your sentence grammatically.

You could use the simple present instead of the first future will, as in

Shyam decides that he will work hard for the upcoming exams and come first in class.

but without a context that makes it clear that you are talking about the future, using future will seems better; by using future will in your sentence it is much clearer that you are talking about future time.

I call will in your sentence future will because the modal verb will has other uses than to talk about future time.