Det lyder som en opgave for LEFT OUTER JOIN for mig, sådan:
SELECT parent.name, COUNT(product.item_id),
(select count(*) from Category parent2
where parent.lft > parent2.lft
and parent.rgt < parent2.rgt) as depth
FROM Category parent
LEFT OUTER JOIN Category node
ON node.lft BETWEEN parent.lft AND parent.rgt
LEFT OUTER JOIN Item_Category product
ON node.category_id = product.category_id
GROUP BY parent.name
ORDER by node.lft
Derved sikrer du, at alle kategorier vises. Bemærk, at jeg ikke er 100 % sikker.
EDIT:Tilføjet undervalg for dybde, prøv det.
EDIT:Fjernet komma