Moving to UK from international school abroad

Fee status is fixed at point if entry. Independent schools are more used to overseas educated students but Us system is quite different and there will be gaps, so they may be able to go back a year if needs be.

Y9 is feasible - although sone subjects will have big gaps. Things like history focus on very different things in England than the US, for example. We've also struggled a little with Geography - simple things like knowing somewhere in on the south coast etc that is expected knowledge, but not always if you've not been brought up in a country.

For the y12. You may find a college that offers the IB a more straightforward transition. A GCSE in English and maths (and possibly 3 more) would make life more straightforward if they were to stay. It's not impossible without tho.

Are you sure these are the years they will be entering. Leaving grade 11 in the US doesn't translate to starting year 12 the following school year. Year 12 is the same as grade 11.

there is not a link between qualifications and international/national status for uiniversity fees.

the requirement is number of years that you have been resident in UK.

The foreign office has a list of comparable qualifications (so THIS score from US High school is equivalent to THESE A levels)

You need to look at the US school that you are attending. International schools need to be affiliated to a registered body and have acreditation. Otherwise your High school certificate is not worth the paper it is written on.

You will have the same problem moving to year 12 I think, (proving the level she is working at) but you should be able to negotiate this with the school/sixth form college.
You may not be able to begin sixth form without GCSE maths and English, and so may need to take a foundation year to do those. (which would mean they did 3 years to do A level and so would solve your uni fees issue)

For arriving into year 9. At one level this should be fine, GCSE curricula don't begin until year 10. But some schools do begin their GCSE curriculum in year 9.
There are big differences in curriculum between US and UK, and so they may find that they are playing catch up in some areas, especially essay writing, and are ahead in some areas.

Another thing to think about is where you are returning to, and if your local schools in that area are likely to have spaces.

I recommend contacting the sixth form in the place that you want to go, and asking them about their entry requirements.

No your fees status remains the same during the course. The entry requirements for international students is different (often easier) than home students as international students provide income for universities whilst the tuition fees for home students do not cover the cost of running the course.

British Unis are very use to overseas qualifications so that shouldn't be an issue, all be it overseas fees could be. You need 3 years ordinarily resident in UK for home fees (some Unis are more flexible than others on what this means) so even coming to Uk for A levels won't be sufficient.

Joining sixth forms , again depending on the school some will be familiar with non gsce options especially in big cities, some may not. You'll likely find your DC is more advanced in some areas and behind in others so pick A levels that align to their existing levels. Or pick an IB or American based school in UK, again easier in some cities than others.

It is very easy to get accepted to a U.K. university without a level results. You will need to pay international student fees though.

In terms of transfer, year 9 will not be a problem.

Sixth form may be more tricky - private would be ok (though they may want a year pre sixth form to make sure they are up to speed with for example U.K. history). State would be trickier.

There are many issues here but the easiest to answer is of course you can go to a UK uni without A levels as you can take the international student route but you will be charged international tuition fees. You dc needs to be resident in the uk for 3 years to qualify for home fees.

In terms of your Y12 child starting sixth form, there are 3 years of funding available. So either the sixth form will accept transcript from international school and your Y12 will be able to move straight to A levels or they do an extra year at sixth form to gain some GCSEs before starting A levels the following September. It is more likely that a sixth form college will offer this option than a school sixth form.
There will be no issues with your Y9 child.
The problem with delaying until university entrance are firstly that you may be liable for overseas student fee rates and secondly that without A levels your young adult may have to take an additional foundation year at university.