For P,Q,R to be collinear, just show that the slope of PQ is the same as the slope of Qr.
Both slopes were solved to be 2t/(t^2 -1), so P, Q,r are collinear.
The area of triangle OPR can be solved by using the Heron's formula since the coordinates of O,P,R are known. Too much algebra.
The length of PR can be solved by the distance formula
d = sqrt[(x1 -x2)^2 +(y1 -y2)^2]
To get the perpendicular from O to PR, apply the formula for a triangle
Area = (1/2)(base)(perpendicular height of the apex from the base)
The base here is PR.
The perpendicular height of the apex, O, from PR is what you are looking for.
Area is the one you get in one of the parts above.
If you have time to do the algebra, go ahead.