We too gave water from the outset of weaning in a free flow cup.
Tbh I never gave DD cereals as she was not bothered for baby rice so for the first few weeks we gave straight veggies or fruit before moving onto BLW. The Annabel Karmel book was quite useful for introducing solids. I was also a lot less cautious regarding introducing foods but we have no known allergies in our family. I do remember the impact on poos though so I'd try to get a few sips of water in at meal times if you can. We took it pretty slowly introducing number of meals and I think that helped.
If you think your DD may be constipated you could try the baby massage techniques. They helped here, especially the I love you movements!