Hi Taryn Krows,
1) You can win buildings in the events that will give extra population. Look on
https://elvengems.com to get a good idea of what upcoming event prizes to save up your candies for.
2) You can also build the Golden Abyss Ancient Wonder if/when you unlock the tech for it in your tech tree. I highly recommed building that and upgrading it as much as possible. It gives lots of extra population and is only 3x3 in size.
3) The same as above goes for supplies, there are event buildings and Ancient Wonders as you progress through your tree that will help you with extra supplies.
4) Another way to get supplies is to build up a good visiting alliance with your neighbors and well as join a fellowship. You will recieve extra supplies each time you help a neighbor who has already helped you. By "help" I just mean clicking on the hand icon at the bottom of a city and choosing either Culture, main house of builder...it is free for you and you get coins for doing it.
5) "Doing Research" just means you haven't unlocked the necessary tech in your tech tree. Visit the book icon and begin to add KP to the appropriate area...the game will only allow you to upgrade things to a certain point, and then you must wait until you have reached a new chapter in your tech tree. It's a good idea to get familiar with your tech tree so you know where you are headed in the game.
Hope that wasn't too much info for you all at once.