You're looking at "help" as a causative verb (there's only a handful of these, so they're easy to memorise). "To" doesn't follow when causative verbs are used. For "help", you can also use an infinitive as the following verb form, with basically the same meaning. This only applies to the verb "help". It's not a general rule in any way.

It depends. It would be hard to think of every instance. In your example, it could be reworded to say the same thing... "contains examples and explanations that will help you improve your.." "contains examples and explanations that will help you to improve..." The "to" is not always needed with an infinitive, and, as in the case you mentioned, can be omitted. It would be correct to have "to" before both "help" and "improve," but the sentence becomes awkward and unnatural.