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.
I hope this can give you a tiny help. ( how to use color-level layout?)

No, They can't be replaced.

xxx地(openly) It is a phrase of adverb. 给(verb) literally means give, for XXX In This Case: 他十分坦率地"给"我讲了他的故事. He openly/honestly told his story for me.

If it replaces 替： the meaning will be different. 替 includes subbing meaning, as preposition can be used as same as 为，给. doing sth for somebody 替我倒一杯茶。to pour a cup of tea for me.
In Your Case: 他十分坦率地"替"我讲了他的故事.here should be verb, He honestly subbed me to telling his story.

If It replaces 为: It usually will mean for..., to.... original: in order to. due to. etc. 
In Your Case：
 他十分坦率地为我讲了他的故事. It makes sense that means He honestly told his story for me in my sake.
 他很不情愿地为我帮助. It isn't coherent, but makes sense. He reluctantly did me a favor.

Some sentences: 她为我写了一封信。 She wrote a letter for me.
她替我去考试。 She subbed me to take a test (Verb). she took a test for me (preposition)
她给我一个吻。 She gave me a kiss. 
她给我做菜。 She cooked up foods for me. 

not all translations are for XXX in sentences. their meanings are similar. When you understand literally meaning you will make sense differently.

In general, According the context, you would easily understand which one is verb which one is preposition. when it is used for verb, it translates as original meaning. When it is used for preposition. it translates as doing sth for somebody. 

Hope this helps.