1. Yes, we have one parameter we call "flow" that does what your GIF shows. We also have a parameter called "opacity" that does what you want to do. To create a brush that behaves the way you want do the following: open brush settings panel (located on the upper right of the screen), go to the "flow" tab, change "flow pressure" to 100%, go to the opacity tab and change "opacity pressure" to 0%.
(we need to improve the brush settings)
2. Yes, use the same brush settings as described above. You can click on "tip" (round circle for standard brush) to change brush tip.
3. We might open source the brush format in the future.
4. Maybe in a distant future. The problem with plugins is that you have one more API to keep backward compatible.
Thanks for testing Leonardo! Please feel free to email me if you have any more questions or feedback: henning.tegen 'at' getleonardo.com