With regard to your first paragraph, were do they get the idea that their conservative mosque culture etc. isn't conservative enough? Why would they think that being even more extreme is the answer or Allah's will?
They probably ran into an individual or group that preached a different ideology - Qutbism for one - and were shown acceptance and understanding, therefore developed an emotional connection with the group rather than with their family (who they couldn't communicate with) or peers (who saw them as different). There were various Salafist organisations in the UK courtesy of Saudi oil money who would hand out pamphlets and talk to people outside mosques in the 90s - my husband and I have run into them - they talked about liberating Palestine from occupation. The Qutbists however were against the Salafists because the Salafists weren't advocating violence and taking the offensive to fight and conquer non-Muslims. Qutbists believe in a different ideology where they think individuals have the right to declare other Muslims as apostates and kill them for not conforming to their particular ideology of what Islam represents to them. This idea came direct from the writings of Qutb, an intellectual and a Muslim who originally had secularist tendencies, went to study in the US for 2 years on a scholarship, returned to Egypt just before the 1952 coup by Nasser, and was later imprisoned, tortured and executed by the Egyptian government in 1966 after trying to assassinate Nasser and by this time had written a pretty extreme manifesto couched in Islamic terms. He was a leading figure in the Muslim Brotherhood, which gained popular support in the 1950s onwards through their charity and community work amongst the rural poor, unemployed etc
Wiki outlines some of the main tenets of Qutbist ideology e.g. the Muslim community (or the Muslim community outside of a vanguard fighting to reestablish it) "has been extinct for a few centuries" having reverted to Godless ignorance (Jahiliyya), and must be reconquered for Islam.
The importance of offensive Jihad to eliminate Jahiliyya not only from the Islamic homeland but from the face of the earth
The Qutbists were out to create some kind of transnational fighting force for Muslims, like NATO for the West. They were quite successful at spreading their manifesto in certain areas where there was poverty and political instability.
Para 2 : Feeling part of a community/society/culture involves a lot more than just the 'surface' stuff. So why is it that their Muslim background isn't giving them that deep sense of belonging? (please note these are also rhetorical questions, I don't necessarily expect you to provide comprehensive answers).
I think it may have something to do with not being sophisticated enough in their thinking to deal with uncertainty and maybe an element of self-loathing for being drawn to the sexual freedom in British culture when this isn't even discussed in their own homes. It's easy to be certain and have a sense of belonging when you are not presented with ambiguity or appealing alternatives, which is presumably what life in some village in Pakistan or India is like - very little exposure to alternatives.
But in the UK there are so many options and so much freedom, and the internal uncertainty that creates is something that many of us navigate as best we can, usually by balancing uncertainty in some areas with a focus on educational or sporting or work achievements, and also by accepting that we will make mistakes and not beating ourselves up too much about it, and accepting that all we can do is try; but I think all that choice and uncertainty causes some people to feel increasingly unsure of themselves, bad about themselves and feel alienated and they then run into these extreme groups that provide them with certainty and a sense of purpose and belonging because charismatic and controlling members of these groups are so convinced of the righteousness of their cause.
Para 3 : That sounds like just being a teenager to me.
Yes - it's a real joy being the parent of one. It's payback for the grief I probably gave my own parents.
Last sentence of Para 4 : I wouldn't know about your teenage years but I do know that teenagers generally, and for myself when I was one long, long ago, that this is the time when one is looking for some big answer to life; some glorious guiding principle to live by, and that sort of stuff.... Also, one's judgement in those years is not very well emotionally grounded.
Yes - I remember sounding off about changing the world and I suppose violence is appealing. I remember befriending a British mercenary I met while doing TA training at university - he had run off to Angola in the 70s when he was about 17 and been shot in the leg, captured, put on trial and sentenced to 16 years in an Angolan jail. The British man who recruited him in the UK was apparently unrepentant about recruiting mercenaries.
Para 5 : I always find it odd that the responsibility for these things goes to organisations/government etc. It is the parents job; with say grandparents, to do this job of providing these character building, self esteem, and what not, needs of children. This being a task starting from day one. I'm not saying this is easy nor that the way society is organised that there is enough time for this, as society seems more focused on jobs and finance than the home.
True - but a lot of parents don't think it is important or don't have the money or time. My parents didn't think it was important or affordable or were at work, but I carved some freedom for myself at university to make my own decisions about this - hence I joined the OTC where you were paid for doing training.
Hence I prioritise this for my own kids along with good grades. For example, even though my 15 year old daughter is fasting she decided to still play tennis and cricket at a school club and is doing ballet while fasting. She is good at kung fu and a competent swimmer. And is currently out with her friends at a movie to take her mind off fasting.