I think it'll be hard to find you since there are a lot of parties to look through, but you can invite people to your party (It's the first option on that menu). You will need the player's ID number if I'm right. The ID number is on the top right corner of everyone's profile so those who want to join need to share that.
Also, I was mistaken. Jewels can be made in the game. I think I pressed another button and it asked me if I wanted to buy some with money and that's how I got confused
If you want to switch unions, go to その他 and select ユニオンの移籍. It will warn you that it costs 100 jewels (the purple medal with the gold star in the center), you will be kicked out of whatever party you're in, and your weekly and monthly lux count will be reset to zero (this won't affect your level). Select the red button to confirm. From there you will go to the heart station and can choose a new union.