I had a go at your second question.
The distance between your particle and the origin |r| and its square will be minimum at the same time t*
I multiplied this out to get
Differentiate the result and set equal to zero to get
Find the three roots of this equation (one is t = an integer)
Ignore the negative root as negative time is silly.
Find |r| for each of the other two roots, one of these is t*.
iii) Find r(t*) from part ii)
Find v(t) = 2i - 2tj by differentiating r(t)
Find the dot product of v(t*) and r(t*). By my calculation the answer is zero proving that they are perpendicular. Could the question be wrong?