Can a simple subject be simple and compound?

it is a verb conncted to a conjunction

Yes. The term "simple sentence" means that there is only one independent clause (thought) within the sentence, not that there is only one subject or predicate within the sentence.Example:"Bill and I...

At least two, unless the compound itself is considered a single simple subject.

Yes. A complex sentence consists of clauses linked by coordination - and, or, but. eg She likes ice cream but Micheal doesn't like sweet things. simple subjects She and Micheal

Mary and Alice ate ice cream is an example. Mary and Alice are the two elements that constitute the compound subject, and ate ice cream is the simple predicate.