All the question about how to achieve a certain effect by using Generateblocks is a valid GB question.
The theme doesn’t have control over the blocks.
The list should’ve shown all the blocks when there’s no block is selected:
https://www.screencast.com/t/xUP6iojpuJ
When a block is selected, it will only show the block itself and its child blocks.
Gradients: yes, it’s easy to do so, just set the color one and color two to 50, and direction 180.
Moving buttons: Moving block is not very easy, I personally feel the user experience isn’t very friendly since I’m having the same trouble moving blocks to the right spot as well, especially when the structure is complicated.
I would recommend saving the button as a reusable block (this WP function is not very stable either, sometimes causes trouble), then add it to the place you want.
If you have GB pro, you can create global style for blocks, and also you could use the copy style from an existing block to a new one, save a lot of time too.