In the example for はなす, it uses the sentence かれのことを おとうさんに はなした。 (I told my father about my boyfriend). I am unsure of what こと means in this sentence as I have not seen it in any of the previous lessons.
In this sentence it is translated as about (わたしの かのじょの こと） about my girlfriend. However, it's not covered until Course 4 Lesson 3. It can also mean a number of other things depending on the context of the sentence.
Koto more or less represents an abstract mental concept, while mono represents actual real things (tangible or intangible).This is kinda hard to explain......
(I'm gonna use an example a friend of mine used before because I like it. ^^)
A difference in mono and koto....koto is the mental concept, mono is the real thing. For example, one's childhood is a real intangible thing, but the concept of having a childhood is not and is purely a mental concept.
koto is common when saying you like somebody.It's quite different from Western languages and therefore has no translation. Say you don't like someone. Simply saying "[person] ga kirai/sukijanai" is really direct. While using koto is less direct as you are more or less saying you don't like the mental concept you have of that person.