First of all it looks to me that it is a conservatory which has a flat roof.
The cavity trays which are now formed in lead with welted stop ends should mean no water is getting in via the cavity/external wall.
But being a flat roof, water can be blown up UNDER the lead flashing on the roof.
There would need to be a stop or secret gutter to prevent this. In addition, the lower lead at the laps needs to have the end turned back on itself again to stop water being blown along the lead and then under.
As for compensation, you need to decide how much is fair and justified and write and claim this.
I would wait until the problem is 100% resolved though.