"...So you obviously wear the niqab insanity?..."

Kindly check my profile...

"...I have heard from many Muslim women that it is not state in the Quran that they are required to wear it. ..."

See there are some people who when faced with truth get into denial mode. Quran is there in all languages and anyone can buy a copy of it and read it for himself.

The clearest verse on the requirement of the hijab is surah 24:30–31, asking women to draw their khimār over their bosoms.[9][10]

And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their khimār over their bosoms and not display their beauty except to their husbands, their fathers, their husband's fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. (Quran 24:31)

In the following verse, Muslim women are asked to draw their jilbab over them (when they go out), as a measure to distinguish themselves from others, so that they are not harassed. Surah 33:59 reads:[10]

Those who harass believing men and believing women undeservedly, bear (on themselves) a calumny and a grievous sin. O Prophet! Enjoin your wives, your daughters, and the wives of true believers that they should cast their outer garments over their persons (when abroad): That is most convenient, that they may be distinguished and not be harassed. [...] (Quran 33:58–59)

"....Also a child in my class actually said that its her Dad that wants her Mum to wear it, however when they travel outside Qatar she is allowed to show her face as 'no one will know her'. Which I find bizarre......"

Yes even I fond this bizarre, because muslim women should wear hijab to obey the commands of Allah (not for showing off piety to public)

"....Also quick question: Is it allowed to communicate with men you don't know on the internet in Islam??..."

hmm...I don't know the answer at present but will definitely get back once I am sure about the answer.