Does Quran teach peace or war?

[Muslim Scholar]

You cannot question Gods' actions, because we don't know how/why God do things?

If this was true, it's better for him to remain silent. We should only implement rules we see the reasoning to. Otherwise, if no reason is apparent, it will seem unreasonable to many.

As I said in the other thread "What is a proof"
There is a difference between Paradox and contradiction
If you can find a single Paradox in a religion, this will falsify the whole religion
but a contradiction can be a paradox/error or a miss-understanding due to lack of information
As God is not similar to anything we know, if he said that he created people to worship him,
You cannot question that as you don't know something similar to God.

If Islam is absolute truth, then it can say killing babies are right and that would be true and ok as well. What's your point?

Yes, God can order us to do anything
God said:
4: 66. And if We had ordered them (saying), "Kill yourselves (i.e. the innocent ones kill the guilty ones) or leave your homes," very few of them would have done it; but if they had done what they were told, it would have been better for them, and would have strengthened their (Faith);

67. And indeed We should then have bestowed upon them a great reward from Ourselves.

68. And indeed We should have guided them to the Straight Way.

69. And whoso obey Allâh and the Messenger (Muhammad صلى الله عليه وسلم), then they will be in the company of those on whom Allâh has bestowed His Grace, of the Prophets, the Siddiqûn (those followers of the Prophets who were first and foremost to believe in them, like Abu Bakr As-Siddîq (رضي الله عنه), the martyrs, and the righteous. And how excellent these companions are!

70. Such is the Bounty from Allâh, and Allâh is Sufficient as All-Knower.
But as God is merciful, most of his commands are rational (not all) to make it easier for us to follow
for example he forbidden drugs and made it harmful to our health.

Also, Quran forbids killing apostates that are peaceful and not at war with Muslims in Suratal Nisa.

4: 89. They wish that you reject Faith, as they have rejected (Faith), and thus that you all become equal (like one another). So take not Auliyâ’ (protectors or friends) from them, till they emigrate in the Way of Allâh (to Muhammad صلى الله عليه وسلم). But if they turn back (from Islâm), take (hold of) them and kill them wherever you find them, and take neither Auliyâ’ (protectors or friends) nor helpers from them.

90. Except those who join a group, between you and whom there is a treaty (of peace), or those who approach you with their breasts restraining from fighting you as well as fighting their own people. Had Allâh willed, indeed He would have given them power over you, and they would have fought you. So if they withdraw from you, and fight not against you, and offer you peace, then Allâh has opened no way for you against them.

God is saying kill them, except if they escaped and joined a group which you have treaty with them.