Transports/Colony Ships and Carriers

Let me first start off by saying I'm new to this game and I'm frustrated/confused about upgrading ships, primarily Colony ship upgrades to transports. Let me explain:

I have colony ships that have become useless, do to planets already colonized. I want to begin invading and taking over the planets. I decide to upgrade my colony ships to transports with the expectation those ships will be my invasion force. All the techs are in place to invade. When I go to invade, no population/soldiers on the ships. Ok, I'll send them to my shipyard, dock them and expect to be ready to invade. Wrong! When I eject the ships, the pop-up to set the population on those ships doesn't show. What am I doing wrong? If someone could explain why I can upgrade the ships, waste the money, and not be able to use them. My desk will thank you for it, because of the beating it has taken lately.

Another question off topic, but one I'm pondering. Can tiny and small ships dock in the Carriers? I created some Carriers and tried to dock a fleet of tiny assault/interceptors in the Carriers and I couldn't. Do Carriers only use a certain ship? Do they come with their own ships? Any answers to both questions, would be kindly appreciated.