How to interpret this PubChem record of L-Alanine
The PubChem format description is not that easy to find:
https://www.ncbi.nlm.nih.gov/IEB/ToolBox/CPP_DOC/asn_spec/pcsubstance.asn.html

And the ASN file linked here:
https://pubchemdocs.ncbi.nlm.nih.gov/data-specification


  I am correct in saying that the numbers in the 'element' array are corresponding to Atomic Numbers? 


Yes, 1 is hydrogen, 6 is carbon, 8 is oxygen, etc.


  And these atomic numbers are assigned to ids from the corresponding indexes in the 'id' array?


in your example, "atoms": {"aid": [1, 2, 3,  ...,  13], "element": [8, 8, 7, ..., 1]},, the the ID of the first atom would be 1 and element 8 (oxygen), the third atom: ID 3 and element 7 (nitrogen).


  Am I correct in saying that these represent the x, y, and z coordinates of atoms in the corresponding index of the above elements array?


Yes


  What are aid1, aid2, and order? 


aid1 and aid2 are the atom identifiers. order is the bond type. 


  These arrays are 12 entries each so each must represent 1 bond between two atoms. But what do the number values correspond to? How should they be interpretted?


For example aid1 = [1, 2], aid2 = [3, 4], order = [1, 2] would mean a single bond between atom 1 and atom 3 and a double bond between atom 2 and atom 4.

Good examples of implementations:


PubChemPy
pubchem_2d_structure_json_to_svg.py