Hi OP, have name changed for privacy, but I have had two DC at Sevenoaks since Year 7, so can give you my twopence worth.
First, I'm biased of course, but it's a really fantastic school.
In terms of 'level', it's very academic, and that's not just down to the international intake. The level at Year 7 is very high too, with many who have turned down places at the grammars ('normal' or super selective). Equally, I know kids at the grammars (incl super selectives) who didn't get a Sevenoaks place. I think the reason it's statistically 'easier' to get into than some of the London schools is about population density and local alternatives - the likes of Judd and Togs are very good schools, and although Sevenoaks offers more in terms of facilities etc, there are lots of people who simply aren't able/willing to pay 25 grand a year for the difference. Also, as others have said, there are plenty of parents who don't want an IB school, or don't want a coed school, which probably lowers numbers a little.
In terms of demographics, from my observations in the pre-boarding years, there are four types of pupil. First, there's quite a big intake from Sevenoaks itself. Second, there are kids from the surrounding Kent villages and towns, or from just over the border in Surrey or Sussex. Third, there's quite a large contingent of London kids, mainly (though not all) from south London, who travel down on the train. Finally, there always seem to be a fair few who arrive direct from overseas - in some cases their family move over just for two years until the child can start boarding in Year 9. Of the local kids, most come from preps, with a handful from state primaries. Generally, they seem to choose it over the grammars because of facilities and extra curricular, IB, coed, class sizes, ethos etc. Some I've talked to from London have said they chose it over London day schools because of the big green campus, and the benefit of boarding school facilities in what (for them) is a day school.
Interestingly, even among the local contingent, there's often a slight international angle. Maybe families who've lived here for years but are originally from Germany or Nigeria or America or Sweden. Or 'native' British families who've lived abroad for a while but are now back in the UK, or who just travel a lot for work. I think that international flavour does maybe deter some parents who are looking for more of a 'people like me' feel - personally I love the fact that my DC sit in a classroom with lots of kids who have quite a different background/outlook than them, but I know that's not for everyone. I do think it's a great choice for a family like yours who will have relocated from overseas, as there will be many others in the same situation.
In terms of exam preparation, I think you've got time. We prepped for both 11+ and Sevenoaks in a year. I would have thought Sevenoaks might be marginally easier in that situation, as they will have a bit of flexibility over their process to be able to take circumstances into account, whereas the 11+ is marked by a computer so is totally inflexible in terms of mark scheme. From what you've said, I think reading reading reading is the only way with the vocab. The Sevenoaks English paper is pretty tough, so you'll need to work on that. All the past papers are on the website, so you've got lots of resources to work through.
As for secondary competition only being an Asian thing, I'm afraid not. London and Kent are madness in terms of grammar and private competition (and for some of the best non-grammars as well).
Best of luck, whatever you decide!