All three sentences involve coordination understood broadly, since all three involve two conjuncts linked by a coordinating conjunction (and). The second sentence is the odd one out, as it is what's referred to as a right node raising construction. Note that in the 1st and the 3rd sentences, two constituents are coordinated:
a. Mary [VP likes ice cream] and [VP hates pies]
b. Mary [VP bought an ice cream] and [VP ate it]
The second sentence, on the basis of the surface syntax, looks like it involves coordination of two non-constituents, since the subject and verb don't form a constituent to the exclusion of the object:
c. [Mary likes] and [Jack hates] pies
Given some auxiliary assumptions then, the bracketing given in (c) can't be correct. There's a number of different analyses on the market for (c), including across-the-board rightward movement of the object from out of both of the conjuncts, and ellipsis of the object in the initial but not the subsequent conjunct. Since this isn't relevant to your question, i won't explore it further.
Your arguments seem to be based on the faulty assumption that true coordination must involve coordination of two sentences which are in a specific discourse relationship with one another, such as cause-effect. Coordination is in fact a syntactic phenomenon - what the coordinated constituents happen to mean is irrelevant. If you take 'coordination' to mean something other than syntactic coordination however, then this is just a terminological quibble. If you're interested in the discourse relationships which hold between sentences, and how this interacts with coordination, you might want to take a look at the work of Andy Kehler, who has explored such issues in a number of different articles and books.