The Quentin Blake is going through something of an existential crisis at the moment and has neither a head nor a deputy head. Don't really want to say more about it on a public thread. However, they don't have a problem at the moment getting enough English speakers for the English half, and in fact the current first grade has three classes instead of the normal two. The language testing has also got a lot more tough than it used to be, to weed out kids who are really German native speakers but whose parents claim they are English.
What class are your DC going into? My DD's class will be third grade next school year and there are quite a few places in the class, partly because a few families moved abroad and partly because three kids are having to repeat the year.It's really a matter of luck.
ZZZen mentioned the Montessori nursery in Dahlem - there are actually two very close to the QB (so very near the FU). One is a large bilingual one run by a freie Träger (my daughter went there for nearly 4 years and had a great time) and the other is a small, private one that only uses English. I phoned them by chance the other day about a translation matter and they were really friendly.
The Charles Dickens in Charlottenburg is theoretically identical to the QB, but is generally acknowledged to be not as good and certainly more German influenced. It's got an excellent new head, though (they snaffled the QB's old deputy head) who seems to be improving things.
To be honest, your chances of getting into the Nelson Mandela are pretty low. They're massively oversubscribed at the moment and I've heard of a lot of English only families being rejected recently. Lol at your description of the head, ZZZen, he's a bit, um, gewöhnungsbedürftig. A friend of mine taught there and transferred because she couldn't stand him.
Chances of getting into the JFK as a non-American and without having been to the nursery are essentially zilch.
If you decide to go for a German-only school in Zehlendorf, they're just about all good, but the Nordgrundschule and the Erich-Kästner-Grundschule have got very good reputations, and Sankt Ursula if you want to go Catholic.
Gosh, I seem to have accumulated a ridiculous amount of surfeit information about the Berlin school system over the last few years...What a waste of brain cells.