1. You don't modify building blocks, you re-create them. You call a building block, make your modifications, and then resave it under the same name.
2. Look into categories.
3. Look at the WordArt Add-In on my site for an example of a custom QAT entry of Building Blocks, in this case AutoText. All of the building blocks were stored in a custom gallery and then a link to that gallery is placed on the QAT. This is all stored in a custom template which is added as a Global Template.

You can build a custom menu, but it is a lot more work than a custom gallery control.