ESE is half way between E and SE. You correctly identified E as 90 degrees. So SE is 45 degrees more than 90 degrees. Half way would only be 22.5 degrees more than 90 degree. So ESE would be at a bearing of 112.5 degrees.
S is at 180 degrees. So the size of the angle between S and ESE would be the difference in their bearings: 67.5 degrees.
The minutes unit should be relatively straight-forward to figure out. The half a degree is worth 30 minutes since a full degree is worth 60 minutes. Hope that helps.