When my family has straight cows' milk, we get extremely gassy and diarrhea isn't uncommon, tummy cramps at the least. When the girls had soy milk (DH and I never liked the stuff

), they got runny poop and gas, nasty-smelling too.

We have to go easy on most cheeses, too; pizza is a rare treat here. (We're still paying this morning for having had pizza last night.

)
That said, we all can eat yogurt just fine; the culturing apparently alters both the milk sugar and the milk protein just enough for us to tolerate it. That's not the case with everyone who has lactose or milk protein intolerance/allergy, but that seems to be the nature of ours. I've read the same about hard cheeses, like parmesan, but we just tend to avoid most cheese entirely since the yogurt is so easy. I've started making my own to save money, since we eat so much of it!
I wouldn't give lots of rice milk at 8 months, but I can't imagine any ingredients in it that would be a problem - more as an occasional drink, certainly not as a substitute for milk/formula.
My kids take Rhino Calcium supplements, which are chewables, but my kids are also older now, not babies. I did do a quick Google search and found some interesting nutritional information about calcium and getting it into the diet:
http://www.homemade-baby-food-recipes.com/calcium-sources.html.