How to access organism IDS, taxon nodes from UniProt?
These are NCBI taxonomy ID's rather than anything specific to UniProt. One way to parse them would be using BioPython via Bio.Entrez, for example:

from Bio import Entrez

def get_taxon_name_from_NCBI_id(id_):
    Entrez.email = 'name@provider.com'
    handle = Entrez.efetch(db='taxonomy', id= id_, retmode='xml')
    records = Entrez.read(handle)[0]
    return records['ScientificName'], records['TaxId']

print(get_taxon_name_from_NCBI_id(9606))
# ('Homo sapiens', '9606')


Of course you could query Entrez directly:
https://eutils.ncbi.nlm.nih.gov/entrez/eutils/efetch.fcgi?db=taxonomy&amp;id=9606

Or even more basically do a manual search of NCBI taxonomy:
https://www.ncbi.nlm.nih.gov/taxonomy/?term=9606