I have never heard the phrase 'to pull marks' before, however, its meaning is perfectly clear within the context of the sample paragraph, i.e., to use a legitimate strategy in an exam, a test or similar that will result in a higher mark being obtained. I would not be surprised if this phrase, or something very similar, is used in many academic institutions.
I have no problem with the use of the two comparatives in the sample paragraph. In my reading each of the two comparative adjectives is describing a different noun, and is not much different than saying, 'the grass was greener, the sky bluer'. If the writer had written, 'it's more easier to pull marks' then I would have agreed with your reservations. However, this article from Yale University (Double Comparatives) even gave me pause to reassess my views with regards to (at least) some double comparatives.
I would have written the sample paragraph like this:
[...] in the paper, there is an entire section dedicated to creative writing. This section usually consists of 3-4 options for a creative writing task, in each of which the student is required to write either a descriptive essay, argumentative essay, or narrative essay on a given topic/title. Our teacher advised us to always select the narrative essay option, as it is easier to pull more marks when you have a story to tell.
Note: In the additional sentence: 'I feel that using a comparative adjective twice here had been wrong', the use of the past perfect ('had been') is incorrect. It would be better to replace it with the simple perfect 'was'. The past perfect is used to indicate an action/event in the past that occurred before a different action/event in the past, e.g. 'I had just eaten dinner when the phone rang'.