You can switch to a convertible seat sooner if you want because many of them are safe for infants too if they’re rearfacing. But you don’t necessarily have to switch to a convertible seat until the infant seat size requirements are met. We switched to a convertible seat at 1 year just because our son no longer looked comfortable and we weren’t carrying him around in it anymore anyway.
Depends on the carrier. You could look it up online. I have the Graco 35. Max height is 32" and max weight is 35#. I typically move my kiddos up to the regular rear facing seat between 6-9 months. When it becomes harder to carry them in a carrier than to take them in and out of a regular car seat.