No. Language is not something that can be "better" or "worse" or in any way objectively be "ranked". This would scientifically be totally untrustworthy.
Going through each of your points:
Language is result of social consensus, so could we say less popular dialects or languages are inferior?
Popularity of a dialect or language depends on so many factors, most of which are purely cultural ones that are only allegedly in any way related to a language. Such prejudices arise from complicated social factors accumulating, but just because you hate a nation and like to make fun of their language because they sound different or "stupid" doesn't make the language a bad one.
Could we rank languages by the average amount of times learners spend to be fluent in it? Ranking them harder and easier?
Not either. Even if it were possible to objectively rate learnability of a language (which isn't so easily possible, because it depends highly on the individual speaker and also at which point you assume that a language is fully, halfway, ... acquired), the size of the lexicon or set of grammar rules doesn't make a language qualitatively better or less good. Both can have advantages or disadvantages - learning lots of grammar rules may seem difficult first, but it might help you expressing things way more precisely than with rather simple and widely applied grammatical constructions.
Could we from linguistics point of view decide on semantics and
grammar, etc; ranking languages on ambiguity, vagueness, illogic,
redundancy, polysemy (multiple meanings) and overall arbitrariness?
This still seems the most reasonable linguistic approach to me, but I am convinced that every language is equally powerful.
For example, there are languages which have evidentiality affixes (so you indicate directly at the verb whether you know what you are saying by having seen it yourself, concluded it by logical reasoning, only from hearsay, ...) so you might think those langauges are more powerful, but still it is totally well possible to express the same in English by means of constructions like "The children must be awake, I hear them talking" or "They say she broke up with her boyfriend".
In general, there is always a trade-off between economy of the language's inventory and economy of the way things are expressed - a small vocabulary and simple grammar may be economic in the way the langauge is less bloated, but at the same time you then need more complicated ways to use it if you want to express the same thing (like English having no evidentiality affixes and making use of syntactic means instead). Conversely, if a language permits expressing a lot of slight meaning differences by explicit linguistic means, this is again uneconomic with respect to the size of the inventory the language needs to have then.
What would you define perfect balance on, what is the optimal ratio of language complexity and expression complexity?
Or simply compare languages based on their culture and historical background or any other possible measurement.
What do you mean by that? Japanese is a worthless language as opposed to Latin because the Romans had a huge empire two thousand years ago? Finnish is superior to English because American metal music sucks? This is totally absurd.
Or based on the average information rate conveyed during speech or written communication?
This relates to what I wrote about the third point: This would still come closest to a linguistically sensible way to measure a langauge "quality" based on efficiency, but since there is always a trade-off between complexity of the language's lexical and grammatical inventory and complexity of the language's expressions to express the same amount of information, there is no objective way to determine the "ideal language".
Linking up with what @A. Toumantsev commented (thanks for the amendment):
It is indeed possible to measure single parameters like estimated size of the lexicon, complexity of inflectional paradigms for certain classes of words or text length in relation to the amount of information conveyed as the paper you mentioned did, and it is as well possible to compare these reults between selected languages.
But it is not possible to derive any sort of objective "ranking" from such comparisons; there is no linguistically motivatable judgement about something like superiority or inferiority of a natural language, neither based on features that are actually measurable and even less on solely socially motivated and therefore linguistically completely irrelevant individual or cultural preferences.
You can not just "rate" a language. You can rate something according to to which amount it suits the purpose it was designed for, possibly also with which efficiency it does so. But language wasn't designed by anyone, language evolved over thousands of years from humans simply using the language, and the purpose which language is meant to fulfill is communication - which does work, in any language, regardless of whether you like the sound of nasals in French or consider a country culturally surperior to another because it has managed to kill more people in the past. (Not presuming this is what you think! Just exaggerating to show why I think this is so absurd.)
Such individual emotions have nothing to do with serious linguistic science, and I encourage you to distrust anyone who makes assertions like "This language is so primitive, just like the people who speak it" or "See, I've been learning that language for two years now and I still keep making mistakes, this language is complicated and useless" or "Well, I think we all agree that Swiss German sounds just ridiculous, real German is so much better" or "Oh no, English grammar is so complicated, who even invented those rules, it is so obvious that my mother tongue does it the way that makes way more sense, any linguist will tell you so". No, just.. no ;)