Peace is a middle purpose and the end purpose is to at least one human know and meet Allah. Quran does not state the end purpose of Islam is peace. peace among believers is needed as a means to Allah be known. even Quran says Allah wanted to create life in the form that some humans be enemies of others:
Said He, Get you down, each of you an enemy to each In the earth a
sojourn shall be yours, and enjoyment for a time(24)
And this verse says peace with all is not purpose of Islam:
Muhammad is God's messenger while those who are with him should be
strict with disbelievers, merciful among themselves. (29)
God is the One Who created seven heavens, and the same [number of
planets] which are like the earth. The Command prevails among them so
you (all) may know that God is Capable of everything. God comprises
everything in knowledge! (12)
Everyman, you are toiling constantly for your Lord, and you will meet
The purpose of Islam is not to eliminate all non-Muslims from the earth at the end of time. The Quran clearly states that humans are free to believe and practice any religion.
We have guided him along the [right] path, whether he is thankful or
There should be no compulsion in religion. Normal behavior stands out
clearly from error; so anyone who rejects the Arrogant ones and
believes in God has grasped the Firmest Handle which will never break.
God is Alert, Aware. (256)
Also, the war and chaos at the end of time are meant to prepare for the global governance of Imam Mahdi (a.s.), who will be the sole ruler of the world for many years before its end. Those wars are like necessary surgeries for the health of a body. Those wars and chaos are not the end of the world. All the earth will have one state, one governance, and one ruler. The wars mentioned are with the rulers and states who are his enemies and not with the non-muslim people.
About the Jinns, please note that they are living around us right now. And after the world ends and the entire universe is destroyed, Allah will create a completely new universe and a new generation of humans and jinn. This cycle will repeat forever and has repeated before us many times. (ref)
About your last question, each human can be better or worse than Jinns, and it all depends on the deeds of each human or jinn.
O mankind, We have created you from a male and female, and set you up
as nations and tribes so you may recognize [and cooperate with] one
another. The noblest among you with God is that one of you who best
performs his duty; God is Aware, Informed. (13)
Jinns, like humans, have free will and will experience either heaven or hell.