Hi Dreaming, I'm a long-time Berliner, both my DC have been to Kita here and are now in primary/secondary school.
It's by no means impossible to get into a bilingual Kita/school, but it's certainly extremely difficult to get into CERTAIN ones.
For a Kita I'd recommend the Montessori Tom-Sawyer-Kinderhaus. It's purpose built with a lovely garden, quite large (ie more places available), state subsidized, so the costs aren't too high. DD2 went there for 4 years and really enjoyed it. Each group has a German Erzieher/in and an English-speaking one. They usually have quite a few male Erzieher, which is always fab. The JFK one in Steglitz is also supposed to be OK, but the culture really is overwhelmingly American and most of the DC there will be going on to the JFK school later (which might be a problem for your DS to lose his friends, as you have little chance of getting in to the JFK main school as non Americans). There's another bilingual Montessori Kita in Zehlendorf but it's much smaller, just Google Montessori Preschool Berlin. I think they're more ideological about Montessori. There's another subsidized but semi-private bilingual Kita in Steglitz called Happy Kids. My friend's son went there and they were fine with it, but not ecstatically happy - there were very few genuinely English-speaking kids, it was almost all German families who wanted to give their DC a 'good start' by increasing their English exposure at an early age. Many of the 'English' Erzieherinnen were Germans who just spoke English to the kids (meaning that they might teach mistakes to your DS - not sure if you'd find that a problem. We also went to look around Happy Kids for DD2 and decided against it in the end because Tom-Sawyer seemed a better option (and has better premises).
I don't know the Max und Moritz Kita, but I've heard about one called Aufgepasst on Blissestrasse - to be honest it looks awful from the outside (in shop premises directly on a dusty street) but it might be a lovely, caring environment for all I know. We used to live in Schöneberg - bits of it are absolutely lovely to bring up a family, other bits are less desirable.
The private schools like Metropolitan and Phorms are all fairly recent and still having teething difficulties, I've heard. Quite a few DC transfer from them back into the state system after a few years. One of DD2's friends had 4 years in Phorms and her parents said it was fairly chaotic (the bilingual system tends to be chaotic anyway, but at least in the state system you're not paying for the chaos except as taxes!) The Amalienhof school is fairly upmarket and more established, but it totally follows the British curriculum I believe, so is mainly suited to families who want/need their kids to have a British education, and to be honest, people who don't really want to integrate into German society (which might be understandable if you're only seconded here for a few years). I think the Berlin British school is fairly similar in its expat culture.
The Nelson Mandela is really popular right now and has far more applications than places. Last I heard they weren't even taking people on the waiting list, but it's always worth a shot. You have more chance if you count as 'highly mobile' and your employer can confirm that. I think diplomat and journalist families also get priority there.
Your best bet of getting a bilingual state school place is the Europe School system - the Quentin Blake and Charles Dickens at junior level, and the follow-on Schiller Gymnasium at secondary (although I'd only recommend the Schiller to a child who is already competent in both languages, as a lot is expected). PM me if you'd like more info on the QB/CD - both of them have what I would euphemistically term 'issues' you should know about before sending a DC there. But then again, the same is true of any Kita or school in Berlin, if truth be told.