After I started the engines, there was one last group of hugs before we disconnected shore services, took in the lines, and slowly made our way from the dock. - I was taught the first comma isn't needed because the clause is part of the sentence and just stating the timing.
I certainly agree that the second set of commas looks like the Oxford comma, on the grounds that the writer is listing three activities which the protagonist is engaging in. The Oxford comma itself is somewhat contentious these days, but I'm in favour of it.
As to the first comma, I think that's one of the few cases where you really can take it or leave it. Neither @Switch Blayde's comment that it is setting off the introductory phrase nor yours that it unnecessarily fragments the sentence is wholly correct or incorrect. I'd suggest that this is a stylistic choice, although author intent may come into play.
If the author is putting the comma there because they really do think that it is a dependent clause, then the comma is likely unnecessary. However, it is possible that the author just wants the comma there as a stylistic choice, but isn't quite sure what the rule is so they say that it's a dependent clause because that's a phrase they know.
Orson Scott Card, who teaches writing at a college level when not writing, once suggested that anyone who speaks English well can also write well, the problem is that most people don't believe they can write so they over-think things. If you just write things down the way you would think things through, then you can fine tune it afterwards.
Since we're looking at somewhat complicated examples, try this one:
Dinner, cake and ice cream, and a fire in the fireplace were all cool.
-- from Living Next Door to Heaven, part 1, by Aroslav.
When I first looked at that I thought that it might be changed to:
Dinner, cake, and ice cream, followed by a fire in the fireplace, were all cool.
On reflection, though, that mildly shift the meaning. Alternatively, you could change "cake and ice cream" to "cake with ice cream", but that might then imply that the ice cream isn't optional, everyone has to eat both.
Eventually I decided that the way it is written probably is best to convey what the author intended, but that it is also a very good example of a situation where it is absolutely necessary for any editor to understand the grammatical rules rather than just go by what sounds right, and where very minor differences in punctuation can shift meaning.
"I was taller than her"
even though to be grammatically correct it should be
"I was taller than she."
Alternatively, since you're aware of the potential issue, you might change it to: "She was shorter that I was.". Which would be correct both grammatically and in how it sounds.
she's Pakistani so she must learn English grammar rules more stringently than us (and British rules)
I've interacted with a lot of people who have learned English as their second (or third, or fourth) language. In general, and this is certainly an oversimplification, there are two major factors which affect how they learn English.
In Central and South America, people get English books primarily from the US, but most of the rest of the world gets them from Britain. This is purely economic; shipping is cheaper from the UK to Europe, Africa, and Asia then it is from the US. As a result, they're are actually a lot more people in the world who learn British grammar and spelling when they learn the language officially. This ignores Commonwealth countries like Canada and Australia which have to print their own because we use variations on British English.
The catch, though, is that the US film & TV industries export a lot more to the rest of the world than the UK does. Historically, large parts of the world had almost no local film industry, although that has shifted in the past few decades. The result is that many people speak English closer to the US way and know more American slang.
This creates a somewhat odd effect. A lot of continental Europeans (and western Asians such as the Middle-East and Russian states) can read and write English very well, but lack confidence when speaking the language. South-east Asians, especially Japanese and Philippinos, are often the opposite: they are confident in their ability to speak English, but lack basic training. Many of them are overconfident, in fact, which is a problem when they come to Canada for post-secondary education and can't understand or be understood by the professors.
I haven't spoken to anyone from Pakistan, but I'm not surprised that your beta-reader falls into the camp of having a good technical knowledge of the language but less of an ear for it.