Also translates to "They should eat", although I don't think this construction has been seen yet
Anything that makes this specifically "they want food", vs. "he wants food" or "she wants food"?
Yes, and no. It's उन्हें, so it's grammatically plural, but it would work if this is said talking about an elderly to whom you give respect. I might be wrong for the use of उन्हें for respect though.
उन्हें बुलाओ can mean "call him" or "call them" depending on context.
उनको is the possessive pronoun = their (with a plural masculine name)
उन्हें = वे + को = to them
No difference. Either can be used for उन [ oblique case form of वे ] + को
Plural masculine possessive pronoun would be: उनके
उन्हें is the 'short form' of उनको. there are other for other pronouns, like मुझको becomes मुझे and others.
technically the 'short form' is the dative form of the pronouns, check out wikipedia for more info: https://en.wikipedia.org/wiki/Hindustani_grammar#Pronouns