Many websites and books offer lots of problems and tasks for mathematically talented students. Can somebody point me out a complete program for work with mathematically talented students aged between 7-15 years?
I have no idea what to do with 7+ children (with the exception of my family), but have some experience in dealing with 14-15 year old children. If they are proud of there talent (even erroneously) it is necessary to determine holes in their knowledge. In any country there are several books for such children. Remind you own books when you were preparing to enter University. Books for good children do not change quickly. However, situation is strongly dependent on the number of children in group. If less than six, you can take care about all of them. If larger than some of them will be lost. My own practical experience suggests that talented children usually quickly be tired of their studies. So during one hour be prepared to have 2-3 short intervals telling something interesting to them, may be not directly connected with lesson. With smile I can claim that children that interest in natural sciences usually are rather unlettered in many other things. This strongly alleviates the problem. Good luck.
My very own personal experience - from once upon a time having been a student in such a group for mathematically gifted children - is that mathematically gifted children are usually not very interested in following a predefined course program anyway. In our case (we were a group of children aged 11 to 15) we very soon discovered individual interests and "favorite topics" and started doing our own projects, in groups of two or three children, with supervision only when we had questions. Oh, there were "curriculum" problems that the kids that didn't have their own plans could do, but frankly, I can't remember ever (!) doing one of those. (I ended up in a small group of young computer freaks that did weird useless geometrical modelling that nevertheless was FUN, precisely because it was nothing that any teacher had ordered us to do!)
Also, is this a mixed group of children aged between 7 and 15? In that case, it will be very, very difficult to find material that suits all of them, unless you stick to topics that are not usually taught at school. Otherwise, the different level of knowledge from school math classes is going to be a problem. Even a gifted 7-yr-old will not have much knowledge besides adding some numbers, and repetitions of school basics are going to bore the older children to death. I'm not sure how this is supposed to work. Anyway, even when starting with a predefined problem, I think you can expect to be faced with lots of unusual and unexpected questions whose answers will lead you pretty far away from any planned lesson content...
Maybe this collection of resources could be helpful when planning your work with these children:
There are two online schools that i could recommend. But they are not free and their price is not so affordable. The curriculum and the implementation are very good in my opinion.
https://artofproblemsolving.com/
https://brilliant.org/
This one is free and is great, but it is not specific for gifted students only