I have no problems doing it in my cooker. I only make one adjustment. My cooker has it's own unique (japanese measuring cup, so you add x number of cups of rice to the bowl, and then fill with water to the line that corresponds with the number of scoops. I never measured the ratio with white rice, so I don't know what it works out to.
Brown rice needs more liquid, so, under the theory that heat is heat, I just follow the ratio on the brown rice package--2-to-1 water to rice. Seems to work just fine (I usually add a bit of oil and some "Better Than Buillion" for flavor, but this wouldn't affect the cooking.
It depends on the rice cooker. My last one did fine, but the current one needs to be turned on for another cycle of cooking. When the bar clicks from "cook" to "warm," I add a little more water and then click it back on again, checking periodically. It doesn't turn out as well as it did in my last rice cooker, which was much smaller (don't know if this matters), so it takes some fiddling to figure out how much extra water to add and how much of the second cooking cycle to utilize. Good luck.