Dear Axel, thank you very much for your support and your quick reply. Unfortunately, I already did all this.
The problem is, the phone was new but the setup went wrong. Apple support couldn't figure out why and recommended to reset the new phone. Which I did, completely stressed out as I was. And then I remembered that I had already taken photos at my son's birthday party.
So I started the new phone again not using the old one as a reference - but since you need an Apple ID to get anything started with Apple, the iCloud took over right from the beginning again. The funny thing - iCloud says the last update was in november but there are Cloud photos on the new phone - and three of the missing photos. So there is the possibility that photos can reappear after a reset - but why not all of them? And how can I get to the lost ones. They must be somewhere in this phone. I guess if I hired a forensical IT expert and spet 700 bucks I'd have them within 24 hours but I was wondering if there are apps for this on the market that don't get you everything a person has ever done with this phone but just the basics and might be cheaper. I'm a private person and a mum who just wants to get back the birthday memories for her eleven year old and his friends (I promised to send them the photos).
Apple support couldn't help. They gave my deleted objects a push and some of the deleted photos came back - but only those which I had deleted on purpose from the Apple photo app, not those I accidentally deleted by resetting the phone to zero.
Anyone else who has an idea?
Thanks in advance!