These are entertaining examples. They are all attempts at right node raising RNR constructions, but they all fail because they treat phrases as simply strings of words and ignore the structure of the phrases connected by "and". Almost all "and" constructions in English, including these, follow the same basic rule:
Conjunction rule: Phrases of the same syntactic category are connected with "and" in between (or among, if more than two), and the resulting phrase has the same category as each of the original phrases.
It is not obvious how this rule applies to give RNR constructions, but Gerald Gazdar showed how a simple, already known extension to phrase structure grammar covers the case of RNR. The extension, used in Categorial Grammar, is to represent a phrase as having category A/B when the phrase can be combined on its right with a phrase of category B to form a phrase of category A.
For instance, "in" and "around" both have category PP/NP (PP stands for Prepositional Phrase and NP stands for Noun Phrase). "the house" has category NP. I can combine "in" and "the house" to form a phrase "in the house", which will have the category PP, by the above scheme. PP/NP with NP yields PP. It is similar to the way fractions multiply together in elementary arithmetic.
But since "in" and "around" have the same category, PP/NP, by the above rule for conjunction, they can combine with "and" to form a new constituent "in and around" of the same category, PP/NP. And now "in and around", since it has this category, can combine on its right with "the house", a NP, and we derive "in and around the house" with category PP.
Or, we could have combined "in the house" and "around the house", both of category PP, by the conjunction rule, which gives "in the house and around the house" with category PP.
So that's how conjunction works in categorial grammar. To extend this to RNR, we need only to create phrases with category A/B by starting with a phrase with category A that ends with a constituent B by removing the B phrase from A.
I'll take a simple example similar to your first one, but one that works. "John loves cooking" is an S (standing for sentence) and it ends in a NP "cooking", so we can form a phrase by factoring out the last constituent: "John loves" is an S/NP, and similarly from the S "Mary hates cooking" we get "Mary hates", which is another S/NP.
"John loves" and "Mary hates" have the same category S/NP, so the rule for conjunction gives a new phrase "John loves and Mary hates" with category S/NP. A phrase with category S/NP combines on the right with a NP to form an S, and we know "cooking" is a NP, so we get "John loves and Mary hates cooking" with category S.
And that's Gazdar's theory of RNR. It's very simple, at least if you're familiar with phrase structure grammar.
Now, how about your example "John is and Mary hates cooking"? To treat that in parallel with the example I just gave, we'd have to factor out "cooking" from "John is cooking" to get "John is" with category S/NP. But that would only be possible if "cooking" were a NP, and it's not; it's the participle form of a verb. "John is" has the category S/Participle, and it cannot be conjoined with "Mary hates", a S/NP, because the categories S/Participle and S/NP are not the same.
PS: I've oversimplified, I see, for the last example. "John is a nice person" is grammatical and ends in a NP, and factoring that out, we'd conclude that "John is" does have category S/NP, contrary to what I said above. So apparently you have to take into account some more detail about the function of the NPs involved -- for instance, whether the NP is a direct object.