Why Allah has not destroyed Iblees/shaitan till now as he has not obeyed Allah's command. Why Allah will punish human being for shaitan mastermind that he is not letting people to follow Allah. My primary objective of this question is to know why Allah has not destroyed shaitan yet.
First part of your question: Why hasn't god distroyed the devil?
[Satan] said, "Reprieve me until the Day they are resurrected."
[ Allah ] said, "Indeed, you are of those reprieved."
The satan begged god to allow him to prove to god that he (devil) is better than man. God delayed the devils punishment until the day of resurrection.
Second part of your question: Why is mankind being tested?
We did indeed offer the Trust to the Heavens and the Earth and the Mountains; but they refused to undertake it, being afraid thereof: but man undertook it;- He was indeed unjust and foolish;-
All of man kind was given the option to NOT do the test, but mankind was foolish, and they decided to do the test, as it's written in this verse.
The only power Satan and his accomplices have is to implant evil suggestions; they do not have the power to force people into evil.
Therefore, any punishment meted out to human being is only due to the crimes they committed exercising their freewill. They definitely have choice to refuse the evil suggestions of Satan.
Since this world was created as a trial and test for man, Satan and his accomplices are one of the means to test man; the test lies in whether people resist the evil suggestions of Satan or are carried away. Consequently, he was told that he would not be able to lead the pious astray.
As emphasized above 'Satan and his accomplices are one of the means to test man'. Therefore, he was not destroyed.
Reference: Satan: His Origin and Purpose
When iblees disobeyed Allah azawajjal, he then asked Allah to give him time till day of judgement to deviate mankind, in order to show Allah that we are not worth what were given(status). [it is a long story which I can't cut short and put it here!]
Shaytan doesn't make us do sins but just suggests us in our perhaps(as far as I can concieve) subconcious mind, which is very suceptible and easily influenced by external factors(which includes music and many other things). He has a quality given to him by Allah azawajjal prior to him being demoted i.e, seductive voice. He uses that in our brain (in islamic terms it is called "waswasa") as I said above, the rest of fault is to us. If we obey that we do a sin and if we don't obey that we get a reward for not performing the suggested sin.
The above is easily explained by the amount of experience shaytan has. From our ancestral father (Adam as) to us except a few, he influenced all mankind(and remember he is not old fashioned, he knows the use of technology more than us, beware of waswasa's.)
We chose to go for the test because if we pass it reward is unexplainabily great and if we fail, the punishment is equally disastrous. The test is just like anyother test which is to adhere to said rules to pass and stick to good practices to gain more rank; because Allah says in Quran (17 - Surah Al Isra[=The night Journey], 21);
Look how We have favored [in provision] some of them over others. But the Hereafter is greater in degrees [of difference] and greater in distinction.
The checking there is a lot more strict!
It is true that Allah must destroy shaytan, but you must notice that possibly allah has not destroyes shaitan because of the humans. In fact allah has not destroyed him because of in order to testing us. In other word i should say that shaitan be excuse or a reason or in instrument for the testing of people. Because there must be an instrument or medium or cause for humans to be tested. Therefore we can note it as testing reason that allah has not still destroyed him.