Mozart Piano Sonatas- When do I use Finger Pedalling?
When do I use Finger Pedalling for Mozart Piano Sonatas?

Is there a specific rule that I must use Finger pedalling in my Interpretations for the first movement or when I see an Alberti Bass Accompaniment?

To use finger pedalling to create a gentle, soothing raindrop heavenly effect.
And when can I use the Damper Pedalling as well?

Any hard and fast rule?

If it sounds good. :p

In all seriousness, it depends on the context. I'd say "finger pedaling" works best when the Alberti bass accompanies a very melodic/expressive theme, and the tempo isn't too fast - an example would be the slow movemvent of k. 545. On the other hand, I wouldn't use it under a faster, lighter and/or more rhythmic theme/motive, like the 2nd themes of Beethoven's op. 31 n°3 or Haydn's Hob. XVI/49. That's just my personal taste, though.

As for the una corda pedal, it also is a matter of taste and depends on the dynamic context. I'd try to develop as broad a dynamic range as possible without its help, and then use it when you need to further than what your fingers alone can do.