You got a right.

b ) is a bit tricky. You have to use a counting trick. Consider any two points A,B along the circle. Then the chord AB splits the circle into a minor arc and a major arc (that is a bigger arc and a smaller arc.) The only chords that intersect AB inside the circle are coords that are formed by one point on the major arc and one point on the minor arc. If there are k points on the minor arc, there are k(n-2-k) chords that can be formed that will intersect AB inside the circle.

This implies that the total number of intersections inside the circle are at most:

you can simplify it further.

c) this is easy; you just need to make the following observation, if two chords share the same two endpoints it is the same chord. If two chords share one endpoint, they have to intersect on the circle and can not possibly intersect in the same point INSIDE the circle. Since you can not reuse one point to make multiple chords that will go through the same intersection point inside the circle, this means that at most chords can intersect in the same point inside the circle.