Electronic – What are the “No Connect” terminals on this multiplexer and what purpose do they serve

"ALS" does not stand for "A low sense", it stands for "A low source". The two lines ALS and BLS provide the means to reference the MOSFET gate drives to the sources of the respective MOSFETs. They are not typically connected to ground. It is expected that there will be current sense resistors to ground. The outputs of these resistors, properly conditioned, are fed back to the input comparator to control the cycling of the bridge.

NPTH stands for "non plated through hole". It is a hole in the PCB that does not feature plating internally, so there is no electrical connection between the layers. They are used to provide mechanical support, hence the "mechanical" keyword that goes with them.

I do not know why they are there, that's an SMD so holes on the pads are nonsense. Maybe they tried to put vias on the pad for better thermal conduction, but that's not the correct way of doing that.

The error that you are getting refers to the fact that these pads, that probably do not appear in the schematic symbol and then are not connected to anything, are too near. To get rid of it you can either increase the minimum allowed spacing in the design rules (bad idea) or separate them more. I'd get rid of them.

What I think you should do is:

• remove the NPTH pads from the footprint
• think if your chip needs extra cooling, then add vias to help that
• connect the central pad to ground via a copper area. If its purpose is cooling you should not use thermal relief, it's more difficult to solder manually but I hope you are using an oven for such a little guy

I usually do not use the kicad libraries for the footprints. If you start making them on your own and keep them you will have a double gain: you learn to draw footprints and you are sure that what you are using is precisely what you need.