In terms of what UK laws she has broken, membership of ISIS is itself a criminal offence. She conspired with two other girls to travel to Syria to join ISIS. That conspiracy is of itself a criminal offence - that is, the agreement that they would do that is itself an unlawful act whether she carried it through afterwards or not.
The power exercised by the home secretary was one expressly conferred by parliament in 1981. It has been on the statute books for over 40 years. It is not an arbitrary power but one that has to be exercised in accordance with the law. The question was whether it was exercised in this case in accordance with the law. The exercise of the power in this case does not mean that the power in itself is not something the Home Secretary should have as part of the overall range of measures available to keep this country safe. The problem with electing populist politicians is that they make populist decisions for short term political advantage, rather that for the good of the country. The answer is not to strip them of powers which, when exercised properly, keep us all safe, it is to not elect populist politicians.
Shamima Begum does not have dual nationality. The Supreme Court ruled that because she could potentially apply for Bangladeshi nationality at the time she was stripped of her British citizenship, that meant the deprivation of UK citizenship was not unlawful. Her ability to apply for Bangladeshi citizenship has now lapsed because she is older than 21. Having been born and brought up here she is now stateless. That arises as a combination of (a) a power that was lawfully exercised at the time the home secretary exercised it, and (b) her own inaction since.
The reason it is important whether there was credible evidence that she had been trafficked is because if the answer is Yes (as it was) that leads on to a separate question, which is whether the Home Secretary should have taken that into account when deciding whether to revoke her citizenship. Even though he didn't, the court decided that this did not make his ruling unlawful. So in effect, the court decided that the Home Secretary was entitled to take the view that even if she was trafficked, she still should have her citizenship revoked.