I think rule 3 is pretty clear: if it's someone who does the action, we don't use "for -ing". I went to London to visit my friends. (correct) I went to London for visiting my friends. (incorrect and unnatural) The "to (verb)" form here is called the infinitive of purpose, and specifically this means the desired outcome of the first action. This safely applies to living things performing the action (note that Applebutter's example for the bridge is in passive voice). When talking about objects (which have neither their own thoughts or desires), "for -ing" describes their function. "What's that for?" "What is it used for?" Here's an example which might illustrate "to" vs "for -ing": "I know that a hairdryer is for drying hair, but I use mine to dry my jeans." (ie. I don't use it for its intended function - I have other plans.) Hopefully that's a little clearer for you. I agree the explanations in the textbook seem to contradict a bit.

You are right that rule 3 seems to be a direct contradiction of rule 1, and rule 2 does indeed seem to counterindicate rule 1. Generally speaking, the infinitive sounds better when used in a generic statement such as "The bridge was built to help people cross the river faster." However, it sometimes makes more sense to say "for blanking" when answering a question. For instance: What's that hammer for? For hammering nails. As far as I am aware, there isn't an easy rule for when one uses one or the other, and usually one will sound better, but both will make sense. I hope this helps.