How can we demonstrate authore feelings by the quotes?
This is a difficult question to answer. While on the one hand, the author of a fiction work does (in all probability) want to express their interpretations of life and living in universal themes that reflect their personal philosophy, it is also true, on the other hand, that narrators cannot be assumed to be speaking for the author (though very often they do).
The problem with trying to find the author's feelings from quotations extracted from A Long Way Down is that there are more than one narratorial voice narrating the story. Within the first eight pages we list to Martin, Maureen, Jess and Martin again (never mind they all sound virtually identical ...). So the questions are: Which one represents the author's feelings? Is the author's feeling an amalgamation of all the narratorial voices? Are the narratorial voices an antithetical force or a supporting voice to the author's feelings? Having said this, let's look at a couple of quotations and analyze what can be determined about the author's feelings from the first-person narration.
It was a logical decision, the product of proper thought. ... [and] it wasn't terribly complicated, or agonized.
All your life you're told ... [about] this marvelous place .... And the one thing you can do to get you there a bit quicker is something that stops you getting there at all.
Being owed an explanation is like being owed money, and not just a fiver, either. Five or six hundred quid, minimum, more like.
If we can agree that it is possible to determine the author's feeling from quotations, even through three voices, then we can examine these three quotes and see what they might tell us. Additionally, we can agree that what you mean by "feelings" (a difficult word as it can mean variously emotional state or opinion or, of course, physical sensations) is the author's "opinions" and analyze the quotes with that in mind. As a side note: if "feelings" is emotional state, then anger, hostility, bitterness, and cynicism are the common feelings expressed in the quotations.
One quick examination of these three quotations does reveal a common thread that might well be identified as the author's feelings/opinions and a part of the overall message he wants to express--or contradict. The thread is that each has to do with logic and reasoning.
The first is obvious: Martin made a decision based on logical progression of thought reflecting upon uncomplicated questions.
The second is inferred reverse logic. 1) You want to get somewhere. 2) You want the quickest way to get there (logical). 3) You take the quickest route (logical). 4) You are stopped from getting there at all. 5) Thus the way to get to where you want to go is not to take the quickest route but to wait it out and take the slowest and longest route (illogical).
The third wraps logic in a metaphor (similes with "like" are types of metaphor) so it is not only inferred but the inference must also be analyzed and paraphrased. Being owed an explanation is like being owed six hundred quid. Thus an explanation is something of considerable value while rejecting an explanation is rejecting something of value that is due you. This metaphor/simile is a logical ordering of complex thought into a simile comparing material value to psychological value.