In sentences akin to "I like to cook and eat" or "John and Jill should come over tomorrow", we have multiple sentence members of the same type which are joined by conjunctions. My question is are these just short versions of complex sentences "I like to cook and I like to eat" and "John should come over tomorrow and Jill should come over tomorrow" respectively or are these conversely, just simple sentences with two predicates and two subjects?
These are simple sentences with a single, compound subject (or other element)
So "John and Jill" is the subject in the first sentence. That is one subject (not two) but it is compound.
"Cook and eat" is another compound, and similar arguments apply. It is a compound of two infinitive verbs, subordinated by "to" to the main clause headed by the verb "like".
These may have the same meaning as two sentences. They may be considered a paraphrase of the longer pair of sentences. But they are not formed by ellipsis or shortening of a structure.