Are πώς and πόςο related to each other, like being the same in a different case, or are they completely different words?
They are different. Πώς is the "how" in the meaning of the way you do something. Πόσο is more like "how much" showing amount or degree. P.e. Πώς μαγειρεύεις; =how do you cook? (In what way, how you do it) but πόσο καλά μαγειρεύεις;= how well do you cook?
All of these question words that begin with ‘π’ are related. That beginning letter comes from the same Indo-European root that gave rise to ‘qu’ in Latin, ‘wh’ in English, and the common beginning of question words in many other Indo-European languages.
There are two πόσο. The first one is the interrogative pronoun "how many" and as a pronoun applies to nouns. This one has genders. It's πόσος-πόση-πόσο.
For example: Πόση σοκολάτα θες;=how much chocolate do you want? Or πόσα λουλούδια έχεις=How many flowers have you got? Or πόσο αλεύρι χρειάζεσαι=How much flour do you need? This version of πόσος is gendered and conjugated normally.
The other version is the adverb πόσο=How (much). This one applies to verbs and is the version we have in the above sentence. Πόσο όμορφος είναι!=how beautiful he is! (Here how applies to is) ποσο μικρό είναι το λουλόυδι;=How (small the flower) is? This version as an adverb is not conjugated and is non gendered (because verbs are not gendered ;) )
Yes, it's ποιου or ποιανού, ποιας or ποιανής for feminine and neuter is like the masculine.
If I want to say "how small ARE the flowers?", will it be "Πόσα μικρά είναι τα λουλούδια;"?
It would still be 'Πόσο... ' and then as you wrote it. You should use the adjective πόσος/πόση/πόσο in agreement with what follows to say 'how many', otherwise use πόσο + adjective / adverb, without agreement, e.g. how beautiful = πόσο όμορφος, how quickly = πόσο γρήγορα.
In English, an adverb can modify a verb, another adverb, or an adjective, and an adjective modifies a noun or pronoun. Are the roles of adverbs and adjectives like this in Greek? In this case in the English sentence, I think "how" is an adverb that modifies the adjective "small" not the verb "is" or "are". In the Greek sentence can πόσο as an adverb modify the adjective μικρό?
It would be Πόσο μικρά είναι τα λουλούδια; because Τα λουλούδια είναι μικρά. Here πόσο acts as an adverb,how, not as the adjective that shows quantity itself.
Is this used only as a true question in Greek? Or (like in English) can it also act as a rhetorical question? (i.e. the speaker knows how small the flower is, but is drawing the listener's attention to it.)