Please check

Here is what the Indian Grammar Nerd blog had to say about "the needful" last year:

It's a usage that anyone who has ever worked in an office in India is probably aware of. "The needful" is one of the more notorious relics that haunt Indian English today. Taken literally, it means "that which is needed". But there's more to it than that. It has the property of making you feel both helpless and annoyed at the same time - helpless because you can't figure out what it is you're meant to do, and annoyed at the condescending tone of the speaker.

In its defense, "do the needful" is a victim of its own good intentions. Used as early as the 18th century in England, it implies respect and trust towards the listener by expecting him1 to understand what the speaker has in mind without actually spelling it out. The problem with this is that it leaves the listener free to decide what the speaker intended, which can, as time has proven, lead to bad things.

While most native speakers have outgrown the phrase, India hasn't, which results in its being labelled an 'Indian-ism' and often ridiculed. To be honest, "do the needful" sounds like something out of a bad martial arts movie....

 

But as far as possible, if you know what you want the listener to do, just spell it out. Save yourself the embarrassment of having to explain what you really meant by stating it explicitly the first time. Quit hiding behind "the needful". The next time you want a sandwich, say "Make me a sandwich".
 

And here is what CNN had to say about it on their Global Experiences site (under the title "How to fix grammatically insane phrases found in common Indian English"):

Try to avoid using the phrase "do the needful." It went out of style decades ago, about the time the British left. Using it today indicates you are a dinosaur, a dinosaur with bad grammar.

 

You may use the phrase humorously, to poke fun at such archaic speech, or other dinosaurs.

 

“Will you do the needful?” “Of course, and I’ll send you a telegram to let you know it's done too.”

There is even a blog called DoTheNeedful.ws that tries to explain Indian English to native speakers doing business in India -- of course, it pokes a little fun too. The blog shared a bit of advise that I keep talking about too.

One common thing you’ll notice that you get overcomplicated grammar forms when they want to say something simple.

Don't worry Sanjay. You are getting better everyday.

Also, Sanjay, the word "Since" in your first example indicates that what follows is a dependent clause. (right, Lewis?) To be grammatically correct, you need to change the period after "competition" to a comma.  However, that makes the sentence very long and complicated, so I would recommend this instead:

My daughter, Aruna, is a student of class IX in your school. She wishes to compete in (instead of "for" - You compete "in" competitions, where you compete "for" a prize.) the science talent competition, but has not been issued the appropriate certificate. Please do so, as she will need them by October 14th.

Another quick note: Is this an American school? If so, we typically use "grades" instead of "classes". As in, My daughter, Aruna, is a 9th grader in your school. (Although, I would state the specific name of the school, just because writing as if you were speaking to someone is considered casual. So this, My daughter, Aruna, is a 9th grader at Garfield and Odie Memorial Highschool.) The organization of educational systems is very diverse. I just spent some time working at a school in Belize (where English is the native language). There, grades or classes are referred to as "forms."