I did for 18 month old so we don't get a small cramped table. If making ADR over the phone, I tell the CM about it and that I need a high chair. If making ADR online, then I request for it as we arrive.
Yes. Our 7 month old went before online ADRs, but I think we said two and a highchair (yes, the highchair was our 3rd person-hehe). I assume you can make those same requests online, but you could do it the old fashioned way and call.
A 7 month old should definitely be sitting in a high chair.
Yes, they'll take down all the details (adults, children, and infants) and any special requests you have (high chairs). You won't have to pay anything for the infants (as long as you don't order anything for them), but they have to know how big of a table you need.