Is it permissible to pay a sum of money to a specific party to obtain an excellent English exam result, for the purpose of getting residency in a foreign country due to the unstable security conditions in the home country?

It is incumbent upon a Muslim in non-Muslim lands to be a good example of Islam, and Islam prohibits deception and forgery. Therefore, it is not permissible for you to forge or buy exam results if these countries stipulate this for granting residency. The existence of kidnapping and killing in your country does not necessarily mean that you are exposed to the same. You can head to a country that does not stipulate this condition, for Allah's earth is vast.