Welcome to the forums, I'm glad you're enjoying it so far. Lets see if we can help you continue to enjoy it.
There are 3 types of expansion, Premium, City, and Victory.
Premium Expansions can only be bought for Diamonds. I believe you get one of these per level of your Main Hall.
City Expansions are unlocked via the research menu. Once you have unlocked the research, you will indeed have to pay coins(or diamonds) to place the expansion.
Victory Expansions are gained by completing provinces, and are free to place after they have been won.
The "Trader" is not a person, but a building. If you click to open your build menu, the Trader should be the option at the top right. You may need to research this building before you can place it.
I hope that will help you proceed. Any other questions feel free to ask.