How can I query Object Properties in an OWL ontology

Question

I am working with the FoodOn ontology and need to figure out if a certain class is somehow related to another class. Typical use case: Can a vegan person eat honey? No, because honey is a subsub class of "invertebrate animal food product"!

I am using the python owlready2 library which allows me to run SPARQL queries and query subclass relations like this:

SELECT  ?class
WHERE
{
  # honey
  <http://purl.obolibrary.org/obo/UBERON_0036016> rdfs:subClassOf* ?class .
  # animal food product
  ?class rdfs:subClassOf* <http://purl.obolibrary.org/obo/FOODON_00001176>
}

This code gives me the full subclass path between honey and animal food product - great.

My problem is, that the relationship is not always that of a subclass. Let's look at "vegetarian food product" using the Protege editor:

We can see that "vegetarian food product" is a subclass of "food product by organism" but at the same time it is also equivalent to 'food product' and (not ('derives from' some ('invertebrate animal' or 'vertebrate animal'))).

If I look at all triples using SPARQL I get the subclass relationship but the equivalentClass is just a bnode:

(rdflib.term.URIRef('http://www.w3.org/2000/01/rdf-schema#subClassOf'),
  rdflib.term.URIRef('http://purl.obolibrary.org/obo/FOODON_00002381')),
(rdflib.term.URIRef('http://www.w3.org/2002/07/owl#equivalentClass'),
  rdflib.term.BNode('5846'))

[stripped some output]

1. Why does SPARQL not return all relationships?
2. How can I query for all classes that are either a subclass of 'vegetarian food product' or related to it by some other object property?
3. Also, how can I query for the 'AND' and 'OR' component in the example above?

I do accept non-python solutions as long as it can be automated. Protege has a DL Query tab but I think that I cannot export the results using the UI...

Thank you!