Good clean fun
Could have done this in 9th grade, though my memory on the specific format of proofs is a bit hazy, since you need to begin with postulates and use all sorts of base proofs. Highlight for my answers.I got through one and two easy enough:
i) By Foot of Perpendicular E, the plane A1AE is perpendicular to line BD (because it's a prism). A1AE is the same plane as A1AC, QED or whatnot.
ii) By Pythagorean theorem, the line AC is 4, angle DAC is 60 degrees and angle DCA is 30. Again by Pythagoras, line AE is 1 and ED is root (3). EC is 3 by arithmetic. Since the height of the prism is root (3), Angle A1EA is 60 degrees, and C1EC is 30 degrees. 180-90 degrees equals 90 degrees.
iii) The hard one. I'd probably just out and guess the answer is 30 degrees. If I had spare time at the end of the test, begin with a plane perpendicular to BC1 at the midpoint of BC1, and similarly with AD, and instead find the angle between those.