A. Yes they do and, though this may sound harsh, are not necessarily authorised.
It will depend on the situation of course, but ideally this should only happen in an emergency. Many children have caring responsibilities, and schools and other agencies must do all they can to support them. This can be an issue even with quite young children. However, if we are talking about more than an occasional example, there should be some other way of dealing with it.
A parent may come to depend too much on their child at the expense of their right to an education. Other professionals may expect the child to undertake a level of care that is inappropriate. A written plan is best, which covers how the situation is to be managed, perhaps agreeing that the child can contact home during the day, or carry a mobile phone in school.
If there are repeated examples which cannot be avoided, perhaps some kind of supervised online distance learning arrangement can be set up so that the school can evidence that they have actually done some school work at home. These sessions can then be classed as an attendance (Code B). However, a parent may need to recognise that their own needs have to be balanced against those of the child. That may not be an easy conversation to have, but just allowing them frequent time off isn’t the best way of avoiding it.