EDIT: Absolute has two meanings:
1. Not qualified or diminished in any way; total.
2. Viewed or existing independently and not in relation to other things; not relative or comparative.
(Source: Google Search)
In general, "X, in the absolute sense", means judging X according to an objective standard, rather than a relative standard comparing it to related thing Y. I can run 100 meters in 100 seconds is (or rather, would be, as I can't) an absolute measurement. I can run faster than you is a relative measurement (probably the same caveat applies). "In the absolute sense" is used to designate an absolute standard in a case where both a relative and an absolute standard could be applied.
As for the first example, it appears to be a (negative)online hotel review. It does not make sense to me either. When people write online, especially if they are complaining, they tend to write quickly, and not check what they wrote for errors.
EDIT: If I were to guess, I would say that the hotel had displayed an aggregate score of 4/5. However, the writer of the first example had a very bad experience there. Therefore, the writer of the first example claims that in their view, the only way that the aggregate score can be reached is if is based on a comparison to something else (a relative standard, rather than an absolute one). Alternatively, the author is using the first definition of absolute, in which case, the first example could be re-written as "I would absolutely not rate this place 4/5" or "There are no circumstances in which I would rate this place 4/5" Note that this is conjecture; more context is needed to be sure of which, if either, is correct. I maintain that in either case, the reason for your confusion is the example is badly written, as it is confusing, not only for you, the English learner, but also for myself, the native English speaker. In either case, the entire phrase "In any absolute sense" can be removed from the sentence without changing the meaning of the example, except perhaps removing some of the zeal and vehemence of the author's condemnation.
In the second and third examples, the usage is the same. Absolute is being used as an antonym(opposite) of relative. You can replace absolute with relative, and that phrase, if not the whole section with reverse in meaning.
In the second example, the speaker is saying that as we learn about a subject, we realize that there is more to the subject than we originally thought. Imagine that there are 10 levels to a subject. You understand one level; thus, you understand 1/10th of the subject. As you study the second level, you discover that there are in fact 100 levels of the subject, so in reality you now know 2/100ths or 1/50th of the subject. Relatively, you doubled your knowledge of the subject from one level to two. However, in the absolute sense, the percentage of the subject that you know decreases by a factor of 5. This may be confusing, which is why the author noted that it is paradoxical*.
In the third example, the author states that the phrase is unusual but correct. Thus, (guessing here, as there is not enough context to say definitively) it is incorrect by the relative standard that it sounds unusual, but is correct on the absolute standard of following all of the rules of English grammar.
EDIT: You are correct, policewala. In the third example, the relative standard is comparing it to the way of expressing the thought(the idioms, as you said), measured by how easy or difficult it is for the audience to understand. The absolute standard to what degree the example follows the rules of English grammar.
*It may also be confusing because the author of the section worded it poorly; I certainly think so. Strictly speaking, we don't become more ignorant on any scale, absolute or otherwise, we simply gain a more accurate evaluation of our level of knowledge, both originally and at its new level.