ask your DR about giving water, but mine told me it was safe to give my son water since he was 3.5 months old. i just give him tap water and not usually too much. he loves to drink out of cups, so i give him a little during the day and after meals.
I don't think that water plays any part in constipation or not.
also, my DR said that giving him a little water would not disturb his normal eating pattern (i.e., he would still nurse just as much). hope that helps.
Actually, i think i have read too that at 7 months (or earlier) you can start giving juices as well.
like 1 cup apple juice diluted with 1 cup water.