Here is one way of setting up serial numbers, 2017 SOLIDWORKS PDM Help - Using a Serial Number as a Default Value
It really depends on what tools your company has available to you, I have worked at companies that use a separate software to manage the data side since we had 50k parts and 40k of them were linked to other parts. It was part of a product configurator that managed all of the data for every solidworks item. ( misys)
Where I am right now it is not set up very well, we use acess97 and excel sheets to manage our part numbers that we manually add and track.
No. PDM Serial Numbers are only available in SOLIDWORKS PDM Professional.
Since we use Pro, I cannot recommend what might work best for your company.