I'm not sure about the first question but for the second you have to maximise

(the square of the distance from the particle to the origin)

in other words find t such that and

NB

for the second part find r(t) at the time you found above then find the velocity of the particle v(t) at the time you found above

NB

Remember if two vectors are perpendicular then there dot product=0 so using those two vectors find it and show it doesn't equal 0