When using an object (ParticleSprite) and "Continuous spray", the angle of the particle is set to the angle of motion. Without an object, the particles are drawn with an angle of 0.
Yes, that's by design. The built-in particles do not support rotation. That's one of the things you might want to use objects for.
When using the sprite as an object and "One-shot", if the initial size is randomized and the grow rate is negative, the particles will flip to a negative size and continue to grow. This does not seem to happen if not using an object or for "Continuous spray".
The destroy mode is 'Fade to invisible'. When using an object they can shrink to a negative size, but the built-in particles are destroyed when reaching a zero size. That's also by design (built-in particles cannot be shown mirrored or flipped).
None of the above is visible during the editor preview.
I think that might be a bug, so best to file an issue for that. The editor preview should match the runtime.
"Angle randomiser" claims to apply a deflection over time, but it adds a random angle every tick.
Is that not the same thing?