First sentence:
(While being || Being) a good person, he (devoured || had been devouring) kittens.
In this sentence I mean that he was always a good person in the past, not only while devouring kittens.
Second sentence:
(While using || When using || Using) the services, (you
agree || you're agreeing) to our terms.
I have seen every of above variants in real agreements as well as "by using …, you're agreeing". What the difference?
Third sentence:
We follow these rules (while providing || providing) the
services.
That means that "we" follow these rules throughout the time we provide the services. Also, is it correct to say "during providing"?
Fourth sentence:
(While being || Being) the main instrument for resolving such
issues, this law must be applied.
So, this law has always been the main instrument for resolving such issues since it entered into force, it is not only for a period of time.
Best Answer
What you must keep in mind is that "while" doesn't only carry the literal meaning of "during a period of time".
For example, the first sentence would read completely differently depending on whether you use "while" or not.
"Being a good person, he devoured kittens" means that he devours kittens because he's a good person. Compare, for example, "Being stubborn as always, he disagreed with us" - it means that he disagreed with us because he was stubborn.
"While being a good person, he devoured kittens" means that the person is generally good, but despite that they devour kittens. Compare "While being stubborn as always, he could see our point" - he was still stubborn, but despite that he agreed to something.
In the second sentence, "while/when" might technically be correct, but it reads awkwardly - something like "you agree to our terms as long as you're using the services". I'd rather use "by using" here - meaning that "starting to use the services carries an implicit agreement to our terms".
In the third one, "during providing" is ugly - you generally avoid two -ings in a row. Otherwise, I think both are fine, though "while providing" reads better to me personally.
The fourth is a bit similar to the first - the meaning flips when you apply "while" to the sentence. So either this low must be applied because it's the main instrument etc. (without "while"), or despite that (with "while").