You can do this, but consider that the LM7805 has to dissipate a lot of power. (It has to kill 19V!)
If the current draw of the 12V regulator + the current draw of the 5V regulator is below 1A you might reduce the LM7805 power dissipation by connecting both regulators in series.
Yes. But you're limited to 1amp total current draw.
That's wasting a HUGE amount of power though, almost 2/3rds of your entire power simply as heat. Bad circuit design, SMPS or a different set up would make much more sense.