1/ What it's meant to communicate in the examples given is the speaker's state of mind either as relative to the situation eliciting his/her comment or as relative to his/her immediatelty preceding comment.
a/ case "C'est fou, quoi" (as in the question); the speaker is expressing a judgement concerning his/her assertion (c'est fou) and that judgement is that he/she is not quite sure to explain/comprehend really what he/she has witnessed and that the best he/she can come up with in the way of an understanding is "this situation is crazy", the word "quoi" meaning "Qu'est-ce que ça peut être d'autre qu'une histoire de fou?" (What else could it be but crazy?).
b/ case "Allez, quoi!" (as in the question); this occasion for using the interjection "quoi" has to do with the situation; he/she can't accept that people in their cars should be blocking the way because of a legitimate reason (breakdown, rush hour, accident,…) and is insinuating that the reason is rather what would be the drivers' slow reactions. He/she is saying in a way "Qu'est-ce qu'il peut bien y avoir pour arrêter le traffic? Ce n'est pas possible, ils ne conduisent pas comme il faut!" (What can be stopping the traffic? That's not possible, they mustn't be driving their cars properly!)
c/ case "Je sais qu'elle a deux enfants mais c'est un manoir, quoi." (as in the question); This case is of the same type as the preceding one; the situation is that of someone claiming to be entitled to a certain living space on the count of having two children; "quoi" is meant to express the speaker's bafflement at the idea that the space available in a country house should not be sufficient for a family with two children.
The types found in the examples from the question have to do with expressing the speaker's state of mind: surprise, impatience, (even) anger, lack of understanding, … There are at least two other types of situation.
a/ The first one has to do not with expressing feelings but with pointing out to the listener a reasonnable deduction while at the same time mildly appealing to him/her for recognising the legitimacy of this deduction. Often this sort of deduction amounts to reducing a complex process to an apparently simpler one, to reduce an explanation to a simpler one. It means, at least sometimes, "en bref", there being no doubt as to the legitimacy of that locution in both the written and the spoken language. The example below should make the use of "quoi" in the present context clearer.
- C'est une femme mariée avec trois enfants et qui fait carrière dans l'enseignement; elle n'a pas pris de vacances ces cinq dernières années et elle a obtenu un prix littéraire l'année dernière; elle est très occupée, affairée avec plusieurs associations, du temps pour personne, une femme en pleine réussite, quoi. (…pour personne, en bref une femme en pleine réussite.)
b/ A second case; the speaker wants to express the matter of factness of a situation, it being either a situation that is part of the context or a situation he/she has just related. This case can however sometimes be assimilated to case "B) a/" above; it may be difficult at times to decide which of the two cases is relevant.
- Ils n'ont plus de chaussures, leurs vêtements sont déchirés, ils sont sales et sans argent, ils vont le ventre vide, il ne leur reste plus qu'à mendier, quoi. (as a matter of fact all they can do is beg)
- -- Il a des problèmes avec la justice, une pension alimentaire qu'il ne paie pas… Il vient de faire deux mois de prison pour escroquerie et maintenant on le suspecte d'avoir volé une voiture dans son quartier; un de mes amis qui est allé le voir dernièrement a été accueilli par des jurons que toute la rue a pu entendre…
-- Oui, je vois, un voyou, quoi.
2/ Personally, I wouldn't use that means of expression; it's par excellence a "gimmick" that appeals to lazy minds, feeble minds and generally minds unaware that the shorthand it represents for feelings and positions in a certain range, precludes a real effort at an extraction out of one's own intellect of a verbal identification of the very concepts that are at the root of his/her feelings and thoughts. In other words, this type of use, on top of the tendency for it to be used as a merely empty leitmotive by some speakers, does not help in the way of developping and keeping an intellect agile in the manipulation of concepts nor able of precise unambiguous communications, two qualities that go hand in hand. As an American adage says "use it or loose it.". Of course, there is not always enough time to muster your thoughts and the terms of a "truer" expression, but when so it's probably better to say nothing.
In speaking and in writing, when in an informal enough contexte, the use as in "B)" seems nevertheless tolerable.
3/ I am not aware of a strong taboo concerning this use, except mine in all circumstances. However, I suspect that few will be those that accept it as a standard means of expression in the whole of what is considered serious writing, in other words professional writing.