Is there a way to create a repeating group of data, where we have:
10 consequential weeks presented - without using the database of weeks - so the weeks come from sort of a formula/logic.
Is there an easier way to sum the values from this group fields - so I can click all of them and do some magic to paste their sum formula? (I don’t believe it exists but I wishfully think).
that helps a lot 
but how to do it.
I have a repeating group of 10 elements (weeks) and inside many nested searches. Is there an easy way to add values from those 10 nested searches per type just by selecting those elements?
Yes, there are ways to aggregate and sum the values.
If you are looking for a solution, I would need more information than that.
There are multiple ways one problem can be solved. So it would really help anyone to provide you solution (not magic) if you can provide exact bubble structure of your app and where are you exactly stuck.