The existence of the Planck length does not imply quantized spacetime, which is still very much an open question in the field of physics. To the best of my knowledge most models still posit a continuous spacetime. cf. https://www.quora.com/Is-time-discrete-or-continuous
AFAIK yes, the limits are known as Planck Constants. It means that we are living in a digital universe.
https://en.wikipedia.org/wiki/Planck_constant
There are also conjectures about a _holographic_ universe.
https://en.wikipedia.org/wiki/Holographic_principle
https://www.youtube.com/results?search_query=holographic+uni...