Learn English – How long is “for a while”

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").

What your advisor wants you to do is let Tom read it and ask what he thinks - if he has anything to add to your report or if he thinks the report should be submitted as it is already written.

However, does your advisor know that Tom shouldn't know about what is going on in the report? If your advisor doesn't know maybe you should have told them that.

Ultimately, what you do is up to you. Your advisor is suggesting that you should let Tom read the report and suggest changes (which, of course, you don't have to make).