The CM's at the ride entrance will tell you when you board the ride.
for boat rides like ITaSW, they can sit in your lap. For rides like Dumbo that go up in the air, the child must 'sit' on the seat, usually on the interior. On AStro Orbiter, the ride is bench that you straddle with yoru legs, so that one you hold the child in your lap. Itis the fastest of all the rides like that , but also has the best view. Maybe a little intense for a seven month old, esp on a cooler night. I think the only other one I'd probably skip is the teacups. I'm pretty sure the only restriction onthe safari ride is that the child can't be on your shoulders or anything like that. You wouldn't want to accidentally drop her in the crocodile pit...
Most rides though the child can sit in your lap.
One other thing, during many of the 3-D type shows there are tiny squirts of water, or bubbles, or smells (also on the Figment ride, along with short a blast of air at the end) I don't think you have to worry about getting soap in your eyes or anything, but if you can figure out where the water jet is located before the show starts, you maybe can shield the child by covering the spot where the water jet is located. I'm making it sound worse than it is....but often if you look carefully at the row of seats i front of you you can figure out where the water squirts from. (You can also figure that the water squirts are aimed forthe middle of each seat, so holding the child to the side is another idea.You can also kind of tell whne you are about to get squirted...like if you see a bottle about to be uncorked....or someone splashing into water -that sort of thing. HISTA is a bit loud, the Bug's life one has spiders, but an infant won't care. Watching the 3-d mocies without the glasses is perfectly fine. But mostly, I think a seven month old will want to fall asleep (nurse?) during these shows.