Question

A point charge is used to determine the electric field around a charged particle. Why is it necessary that the point charge does not affect the position of the charge being tested?

Answer 1

The strength, and possibly the shape and direction, of the electric field
around a charged particle depends on the location of the particle. 

If the process of measuring the field causes the particle to move, then
the measurement you get wouldn't mean anything. 

Your measurements wouldn't show the ACTUAL field around the particle.
They would show what the field is like AFTER something comes along
and distorts it, and that's not what you're trying to measure.

It would be like carrying a flame thrower into a freezer when you go in
to measure the temperature in there.

Or if you had to measure how much light is leaking into a dark room,
and you carried a flashlight with you to see your way around in there.