they are tough on the German because if you are not able to read and write it to the standard they require, you simply cannot continue through secondary in particular covering more literary subjects such as history in those languages or indeed learning French/Latin etc which will require translation into German, correct German obviously. The curriculum is very full for secondary. Teachers I know who are German say it is literally impossible to cover the curriculum for a school year within the school year. Therefore the child will have to do a great deal of the secondary schoolwork at home. A lot of school time goes on testing, trips etc so dc have a lot to do at home.
The German school system does seem rather child unfriendly in that there is little scope for the teachers to accommodate dc who for whatever reason are not making the grade (as in passing the weekly tests to a certain standard), this is why IMO they grade and assess them so much so yes keeping them back a year, sending them down to a lower achieving type school etc is still common practice.
So that's the system. Gymnasium is of coure the strictest on grades and the most demanding in terms of work done at home. I am trying not to make a value comment on it but I think to put yourself in your 13 year old's shoes what this will mean is that a lot of school time will be writing dictation in German and doing vocabulary tests in various foreign lanauges (incl. English of course, here he has to give the translation the teacher has taught, not anything which would be possible in English), maths tests, tests at the end of each topic covered in other subjects. They test them all year and the results are calculated to get a yearly average which decides whether they can move up.
That's gymnasium and realistically, I find it hard to imagine a dc with no German managing it. Possibly if ds got a place, he would have to repeat the first year. You can explain this in terms of acquiring enough >German to confidently proceed with subjects so I don't think this need be too much of a blow for him.
I would be reluctant to give up a good grammar school place in the UK to send my child to a German Real- or indeed Hauptschule. In fact I would not do it. So find out where he would be able to go/have to go and weigh up the pros and cons. There are state Gymnasia (you apply directly to the school, they look at grades and otherwise it's up to you to convince them to take your dc. They are all over-subscribed. Then there are faith schools - evangelische Gymnasia, katholische Gymnasia where it probably helps if you are a memeber of a protestant or the RC Church, respectively. You apply directly to the school and it is up to them who they choose. They are over-subscribed. There are some private schools - cheap cf. UK and not that great IMHO on the whole. There are Gesamtschulen (comprehensive) where dc will be in classes acoording to perceived ability yet all together in one school and therefore considered comprehensive. So ds could be in the Hauptschule-branch of a comprehensive. Not good IMO.
Then there are bilingual schools or regular German state school with a bilingualer Zweig - bilingual branch so one or two subjects are taught say in English.
For the smaller dc, there is zoning and the dc will be accorded a place based on where you live. They vary enormously so really you need to find out by asking about if it is ok or look at it and if it isn't, you need to deregister at that zoned school by filling in a formular there, handing it in to the school office and writing in that formular the name of the school to which your dc will be going instead.
I might look at Montessori for the younger ones (primary) which I would take over a regular German state school personally but the problem is at some stage you need to change school system for secondary, so depends if you'll just be there for a year or two or "for good".