Strange Ideas in Grammar

I don't know whether there are any natural languages that do these things, but my brain just comes up with this stuff...

What if there were a language with both prepositions and postpositions? Would certain words always be prepositions, and others always be postpositions? Would some words be able to function as either? If so, what would determine when it could be used each way? Would a given word have a different range of meaning as a postposition from what it would have as a preposition? Perhaps the surrounding grammar would determine the word order. Perhaps prepositional phrases would function as nouns or adjectives, but postpositional phrases would function in other ways (e.g., adverbially). Or perhaps some other factor would determine the word order. Maybe prepositions would introduce their phrases when the speaker is happy or content, but follow their objects in postpositional fashion when the speaker is angry, sad, or nervous. Or maybe postpositions would be more formal and polite than prepositions. Or vice versa.

Then there's case. Natural languages have a fair variety of different case systems. Some languages, like English, barely even HAVE a case morphology, because everything is determined by word order. Greek is practically the opposite: word order has pretty much nothing to do with case, so it's all determined at the individual word level by case endings. In Greek, case is determined pretty much just by function: direct objects are in the accusative, for instance, irrespective of the rest of the structure of the sentence. There are exceptions to that simple rule, of course. Certain Greek verbs, for instance, take what we think of as their direct object in the dative case. Still, though, it's the role of the noun as the verb's object that is determining its case, and that selection doesn't change to accommodate other aspects of the grammar of the sentence. I think I would say the same of ergative-absolutive systems: even if the subjective case varies depending on the transitivity of the verb, it is still the role of the noun as subject of a given verb that drives its case selection, so while it's more complex than a straightforward subjective/objective case system, it is guided by the same basic principle. However, what if there were languages that determined a noun's case by not just its role in the sentence but also other factors? What if the mood of verb, for instance, determined case roles, so that e.g. in a subjunctive clause the subject were in the case that would be used for the indirect object in an indicative clause? Or what if a combination of case and word order determined function, so that if the first major noun in a sentence were the subject it would be in a certain case, but if the second noun were the subject it would be in a different case? (There could be whole systems of word-order/case patterns, so that SVO sentences would, say, put the subject in the A case and the direct object in the B case, but OVS sentences would put the direct object in the B case and the subject in the D case. This sort of thing could even be combined with mood-driven case selection as above...)

And what if there were a language with an extremely small number of verbs, perhaps just one (a linking verb, presumably), with actions specified periphrastically using other grammatical constructs, such as adjectives? I can just imagine the kinds of sentences you could get... Instead of saying that someone ran, you would say they were fast. Instead of saying that Bob gave Mary a box of chocolates, you would say that Bob was generous and then there was a box of chocolates in Mary's hands. Replacing verbs that carry more meaning would require more acrobatics, but I'm convinced it would be possible to say just about anything in such a language, with sufficient noun and adjective vocabulary, once you got used to it.