OK, I advise families moving to and from UK about school entry etc.
There are a lot of points raised by your post.
Depending on your circumstances, you may not need ot wait for the 3 years. If you are UK based, but have been working overseas, you can still claim residency for uni fees. Ultimatley it is down to each uni, some are easier than others, and they require different proof, eg some consider having a house here of evidence that UK is your permanent base, others don't require this. In order to claim you need evidence from your employer that your contract overseas was not permanent and that you always intended to return to the UK at some point.
Second point. Entry to schools at year 7 and 12 is both easier and harder.
Easier because all the places are up for grabs, so you get a chance of a place, but harder in that in order to apply you need to be resident here.
year 7 - you must be resident (not just having an address but living at it) on October 31st of year 6, which is when the applications have to be in. If you are not resident but have an address and use it, you may lose your place due to fraud. If you apply and say you WILL be resident but are not NOW, etc, they will process you as a late application, ie, all the places are given out and then you get what is left. It is illegal to apply of you are not resident at the address.
Some LA will check, (especially in areas of high demand) and some won't bother. Any application after 31st October is a late application and processed after all the other places are given out. The places are allocated by the Local Authority, not the school.
year 12, applications vary, usually Jan/Feb. This is Sixth Form entry for A levels. You will need GCSE or equivalent. If they are not doing IGCSE where you are, then you can find what the equivalents are on the foreign office website. Cut off days for applications for sixth form don't really apply. There is usually a minimum entry requirement. Some sixth forms are school based, some are separate sixth form colleges. Either way everyone has to apply for the places, and it is based on GCSE results. So you are offered a provisional place assuming you get your results (results come out in August)
If you return in other school years, you do a mid year application. You can do this from where you are, but some LA will insist you wait until you are in the country.