Should I add water to my homemade orange juice?
Does water affect the conservative value:

I doubt adding water would noticeably hurt the conservation value, but you could always add it to an actual serving, instead of pre-mixing it.

Does water affect the nutritive value:

It would of course go down per serving. Less juice in the same serving means less of the nutritional / healthy stuff in said serving.

What kind of water:

I would just use plain water. Mineral will dilute the taste even more than regular water, and actually create a different kind of drink.

My take on it, and thus a personal con:

Don't do it, unless you really can't take the acidity of fresh orange juice. The cheaper hotels tend to do it to create more bang for the buck (from their perspective), and I absolutely hate it. The taste suffers, and, for me less important, the nutritional value suffers. To my mind, orange juice with water lacks everything that makes orange juice delicious.