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Plus explanation. From sources, I've heard that those are
I may be wrong.
Would anyone please correct or confirm 1-5 and answer 6
The words that end in -cracy are from Greek -κρατία, which is κράτος 'power' + an abstract noun suffix -ία. The ones in -archy are analysable as ending in -αρχία, or ἄρχω 'to rule' + the same suffix.
In democracy, the initial word is δῆμος 'people'; no surprises there.
Metochocracy uses μέτοχος 'partner, accomplice' (μετά 'with' (in this case) + ἔχω 'to hold' + -ος, a noun-forming suffix), which is certainly a defensible choice.
Monarchy uses μόνος 'only' and is obviously a cromulent word. (Actually it's not μόνος + -αρχία but μόναρχος lit. 'only ruler' + -ία, which explains the semantics a little better.)
Ependocracy looks like it's built on ἐπενδύω, but that means 'to put on (a piece of clothing) over (another piece of clothing)'; only in modern Greek does it mean 'to invest'. A reasonable Classical alternative might be προστίθημι, which has a basic meaning of 'to put to' and from there 'to augment' and in the medial 'to associate with', which I think works. The derived agent noun, προσθέτης, is not actually attested in a meaning anywhere close to 'investor', but I think a coinage like prosthetocracy is defensible for 'rule by investors'—an ugly word for an ugly concept.
Pelatarchy is built on modern Greek again; πελάτης is 'one who approaches' in Classical Greek (ultimately from πέλας 'near'). ὠνητής is a Classical word meaning 'buyer': onetocracy /oʊnɪˈtɒkɹəsi/.
Your last one is kind of tricky because the usual Classical words for tax are τέλος or φορά, which are very ambiguous out of context. Here modern Greek can help: the modern word for taxpayer is φορολογούμενος, the medio-passive present participle of φορολογέω, which Classically meant 'to levy tribute from', i.e. 'one from whom tribute is levied'. That works just fine: phorologoumenocracy.
Obviously none of these except democracy and monarchy will be particularly transparent to anyone.
