Discovery is said to be brand new, yet its registry number (NCC-1031) is lower than the Shenzho (NCC-1227), which was already said to be old when Michael Burnham came aboard 7 years prior to these events. As registry numbers are assigned sequentially, Discovery having a lower registry number than the Shenzhou should not be possible.
The matter synthesizer announces that the matter synthesis of Burnham's provisional uniform is complete as she is finishing zipping it up. The uniform would need to be fully synthesized before she could put it on.
Everyone blames Burnham for starting the war, but, while she did commit mutiny, she was caught before she could enact her plan for dealing with the Klingons. Her actions did not extend beyond the bridge of her own ship and had no effect on the engagement with the Klingons.