coco peat is basically the same thing, except that the peat is a courser grade that may include things like coco chips, while coco coir is very fine. Coco peat has basically a similar texture to peat moss, but still has all of the wonderful properties of coco coir.
I would go with the 5 gallon if you are going to be flowering a well established plant like a mother, because your roots are going to expand in unexpected ways and you do not want them to be limited by the space they have.
You do not have to use RO or distilled water but i would recommend letting all of the chlorine evaporate for 24 hours before mixing nutes and feeding your plants. Depending on how hard your water is, it may not be a problem at all because coco acts as a buffer but actually requires a bit more calcium in order to fully buffer and release nutes, so if your water is hard with calcium, which most hard water is because of the limestone located deep in the earth, then it may actually be benefical. Just make sure that you watch your plants for any signs of lockout or deficiency, and remember that the first places to look in coco are N, MG and Calcium, then you'll be fine.