Welcome Zenny,
Ooh catenatives, my favourite, I like you already.
I looked at this and thought it would be easy - then I realised that there is an awful lot of complication here.
When a verb is followed by a gerund meaning tends to be more passive, introspective and emotional; when a verb is followed by "to" and the infinitive, meaning tends to be more active, deontic and purposeful.
Where there is little change in meaning the difference that remains is that the gerund signifies the activity itself, and "to" and the infinitive, the purpose of doing the action. The situation is altered here because the two different prepositions subtly alter the meaning.
I think they need to be looked at on a case by case basis.
"I'm afraid of flying," means I am afraid of this activity.
"I'm afraid to fly," is more purposeful - I'm afraid of deliberately putting myself in a position to fly.
I'm afraid of crashing is likewise passive, but why would you deliberately crash? The strange thing is that this even sounds strange when talking about a stuntman, but I don't know why. (I've an inkling that this and the other complications have to do with actionsart which is probably a word you don't understand and nor do I fully, I'll try to get back to you on that.)
The next seems streight forward. A mistake must be semantically passive so has to be followed by the gerund. "Afraid to make mistakes" means that you would deliberately try to make mistakes while speaking which is illogical. "I'm afraid of diving into" and "afraid to dive into" the swimming pool both sound correct, although "afraid of" somehow sounds slightly more natural. This is an irritating effect with a number of catenatives.
"Fall" is similar to "mistake" - you can't fall deliberately, it must be an accident - if it's deliberate, then you are jumping.
The strangest thing about these cases is that usually the catenative governs the form of the verb that comes after it, but here the following verb clearly governs the choice of catenative.
I hope at this point that you are in fact a teacher not a student because this won't mean much to you if you are a student.
Now I'm going to have to figure out how all this relates to my website:
http://www.geocities.com/endipatterson/Catenative.html 