Question: Below are just 2 example sentences for the general format '[phrase]地给[noun][verb][phrase]'. 

1. 他十分坦率地给我讲了他的故事.
2. 他很不情愿地给了我帮助.

This type of sentence is very common in Chinese. I would like to know if, generally speaking, it is acceptable in Chinese to replace '给' with '替' or '为'. If you are Chinese, would you find that acceptable in most, if not all, cases?

Answer: 
No. The words have different meanings.

Let's look at your first sentence:
他十分坦率地[给]我讲了他的故事 : He openly told me his story.

If we were to replace 给 with 替:
他十分坦率地[替]我讲了他的故事: He openly told his story for me (implying that I was supposed to be the one telling the story).

If we were to replace 给 with 为:
他十分坦率地[为]我讲了他的故事: He openly told his story to me for my sake. 

In general I'm not too sure how you got the idea that they are interchangeable.
They are not interchangeable. The latter two have fairly narrow meanings in that kind of context: 替 means "on behalf of"; it could be translated as "for," but only in constructions where it clearly means "on behalf of," as in "He did my work for me."

為 wèi means "for the sake of"; again, it could be translated as "for," but only in constructions where it means "for the sake of," as in "She took care of the financial matters, for my peace of mind."

給, on the other hand, has a whole slew of meanings, only one of which is "for." More generally, it can be used simply to indicate the indirect object of a verb, especially (but not exclusively) when that object is the "recipient" of something. That is more or less the way it is used in your example sentence.