No reason you can't use both fruits for the same batch. Better yet, send me the blackberries. I'll mix them with my raspberries and let you know how it turns out
I would add some fruit to the primary and some to the secondary but adding at either stage is fine, each will give you slightly different results / tastes but its all good. Your method for using berries in wine will work just fine. But no need to use sulfites (fruits have natural sulfites, no need to add extra). Unless you're going to back sweeten, then you'll want to stop yeast activity before sweetening.
D47 will probably take your mead down to 1.000 give or take. So if you want a sweeter mead, you'll need to backsweeten. I prefer semi-sweet to sweet melomels over dry ones, but that's my personal preference.
Your water shouldn't be a problem, just make sure it doesn't have chlorine. You're good to go with those containers for fermenting.