Will you believe me if I claimed that I can make two parallel lines intersect? how?

sure. either you perceive them as intersecting as a result of a focal point or they are placed on a curved surface.

Since the question is will I believe you, the answer is No.

Generally parallel lines do not intersect. Sure if the lines are in the same place one could argue they they intersect, but since there would be no way to distinguish one from the other one could also argue there is only one line. But again, the question is, "would you believe me if ..", not "would I be correct if ..." so my answer is therefore correct

Sure. Depending on your point of perspective...for example, two ordinary parallel lines which are NOT on a curved surface, still must be able to exist on the same plane. As co-planar lines, if you tip the plane toward your point of perspective, you will reach a point where both the lines merge into one line, meaning that they will be completely intersected.

NO, by definition two parallel lines never intersect!!

Next question.

I will not agree as the definition of parallel lines dictates that they will not ever intersect. If two lines intersect, that would make them classified as perpendicular lines.

By reading all the answers, I get the point that none of the users had ever done Calculus. Let me give you an equation

y = 1/ x plug in the values for x from 1 to infinity (x value increasing) and again from 0.1 to infinity(x value decreasing)... draw a graph.... you will see what I am talking about.... I know you cannot plug infinite numbers so try with ten numbers... a Pre Calc or Calc I level course will answer your query.

Using the supposition that parallel lines are always equidistant, wihthout considering the nature of the surface, yes. Draw the lines on a sheet of paper and twist the paper.

If you made two parallel lines intersect ....NOW they are perpendicular dude!!

Place them onto a curved surface.

No....idk