1. I will help him.

2. I shall help him
3. I shall[stressed] help him.
--------------------------------
Q1: When 'shall' is stressed, does #3 have stronger volition of the subject? (stronger than #1 in meaning?)
Q2: What is the difference between #1 and #2? #1 indicates the volition of the subject. In #2, is it just a simple future tense?

Yes, 3 and 2 mean the same.

1 is stating a future act, while 2 includes volition. (1 is future simple case.)

A little-known fact is that

"shall" is used for first person:
I shall arise and go now.

"will" is used for 2nd and 3rd person.
They will have a great time.

These are reversed in the imperative mood. That is why the Ten Commandments read

Thou shalt not steal.
The "shall" in the 2nd person indicates command, rather than just declaration.

Sadly, as with most of the rest of English grammar, these rules are mostly unknown or ignored.

English grammar is much simpler than that of many other languages, probably due mainly to laziness and ignorance. While it is sad, the upside is that we have a nice, (mostly) simple grammar, and still manage to be understood, just at the price of more required context.

Q1: When 'shall' is stressed, does #3 have stronger volition of the subject? (stronger than #1 in meaning?)

To analyze the strength of volition between the sentences, we need to consider the context and the emphasis placed on the word "shall." When "shall" is stressed in sentence #3, it indicates a strong determination or a strong intention on the part of the subject. This emphasis suggests a greater level of commitment or resolve to help him compared to sentence #1. While sentence #1 still conveys a willingness to help, the stress on "shall" in sentence #3 increases the sense of determination and personal dedication.

Q2: What is the difference between #1 and #2? #1 indicates the volition of the subject. In #2, is it just a simple future tense?

In sentence #1, "I will help him," the use of "will" indicates a simple future tense. It suggests a general intention or willingness to help him without specifying any particular strength of volition. It is a straightforward statement of the speaker's intent to assist without any emphasis on intensity or determination.

On the other hand, sentence #2, "I shall help him," also implies a future action, but the use of "shall" suggests a slightly stronger expression of volition compared to sentence #1. Although the difference in strength may be subtle, "shall" implies a stronger commitment or obligation on the part of the speaker. However, it is important to note that the distinction between "will" and "shall" can vary depending on the context, regional differences, and personal preferences. In some cases, the distinction may not be significant or may have different nuances.