You should be the happiest man already because I gave you a good solution.

One of those two devices is what you want. They both have midi ports and they both convert the digital data to analog signals that can go into your PA system.
You can buy a cheaper midi-only port like your friend suggested, but you wouldn't have a good way to get your sounds out to your PA. You definitely do not want to use the soundcard on your computer. So, this is why I suggested devices like the two examples I gave. They do midi as well as digital to analog conversion.
Your diagram is incomplete, it should look like this....
casio ctk-700 keyboard (midi) ----> midi/usb cable ----> laptop ---> Audio interface----> PA System
Then you'll need a software program that accepts the midi input from your keyboard and hosts whatever softsynth you are using. For that, I don't have any recommendation. There will probably be a lite version of a popular DAW that will come with either device, but I don't know how well they will work for a live application.
As for your last question. You can buy a keyboard controller that plugs directly into a usb port, but you'll still need a quality audio interface. Only now, without the midi requirement. Check out these two for around the same price.
http://www.sweetwater.com/store/detail/KeyRig49/
http://www.sweetwater.com/store/detail/Transit/