Who is doing the thinking?

Question

Observe the change:

彼女は行かないと思う。 "I think that she will not go"

彼女は行くまいと思う。 "She thinks that she will not go"

彼女は and と思う are conserved in the sentence, yet the person who is doing the thinking is different.

(Question 1) Is the use of the negative volitional form the direct cause of the change?

(Question 2) How do I make specific the person who is doing the thinking in each case?
I.e. How do I express "I think that she will not go" using 行くまい and "She thinks that she will not go" using 行かない?

Answer 1

(Question 2) How do I make specific the person who is doing the thinking in each case? I.e. How do I express "I think that she will not go" using 行くまい and "She thinks that she will not go" using 行かない?

彼女が行くまいと(私は)思います。

and

彼女は行かないと思っている。