grammar - Comma before "with," "who," "having" for non-compound sentences

I've noticed my résumé and cover letter have multiple sentences like the ones (slightly edited) below:

1. I offer excellent computer skills, with a typing speed of 80–120 WPM.



2. I recently met ____, who advised that ...


3. I bring a strong awareness of ____, having completed ...


4. I assumed additional ____ at ____, where I also ...


5. I am seeking entry into ____ at ____, with an aim to ...

I want advice on this that is not "commas are a stylistic choice" — for me, whatever I start doing regularly, I become stylistically accustomed to.

I asked my career counsellor at Stanford and she told me that I should look at what follows the comma as an "aside." According to her, the comma here is correct and should be looked upon as a lone, pairless, bracketing comma. Taking sentence 1, she said it could be thought of as :

I offer excellent computer skills, with a typing speed of 80–120 WPM, and therefore I deserve ____. (Hypothetical sentence with bracketing commas)

I offer excellent computer skills, with a typing speed of 80–120 WPM. (Lone bracketing comma ― period replaces second comma for the pair)

Her second bit of advice was that if I can put what follows the comma in parentheses, then I should leave the comma in.

Going on this, I've removed commas for sentences 2 and 5.

But I'm still confused. Mainly because this rule seems a bit flimsy and could be used to justify commas that are clearly wrong.

Example: "I am good at reading, and writing."

To me, the rule is that only two sentences that can stand on their own when joined together with "but," "and," etc. may have a comma. According to this rule, only no. 4 requires a comma where there is a subject on both sides.

Could someone offer guidance on this?