Cultural understanding of Penelope's suitors

Is enough known about the culture Homeric Greece to definitively explain what's going on, or is it subject to interpretation?

No. Enough is not known. All history is subject to interpretation. Here however the interpretation being requested is improper. The bow of conjecture is too great for History to be able to string it. Particularly in relation to a multiply redacted document making a claim about a purported single exceptional instance.

The interpretation of mythic cultural texts in the way you’re proposing is impossible to do historically. Other humanities may be able to assist you, classics and literary criticism off the top of my head.

Actually, it is quite easy to understand even from today's perspective :

• Penelope still has presumably living husband. There is no definite proof that Odysseus perished, and Penelope refuses to declare him dead. It is entirely in her right to do so, even in modern times.

• Odysseus has a son and heir. Telemachus would legally be new king of Ithaca if his father is dead. Even if inhabitants didn't want him as a ruler, they didn't have right to rob him of his father property. Instead, as you mentioned, some of them even plan to kill him.

• Abusing hospitality. Suitors were living in Odysseus's home for a long time, essentially uninvited and unwelcome. This would be considered unappropriated and even illegal both then and now.

• Penelope was not attracted to anyone of them, and they were not worthy of her hand. It is given that suitors were nowhere near manly as Odysseus. Indeed, at the end of Odyssey, they were tested with Odysseus's bow, and none of them could draw it. Yet, they are forcing themselves to Penelope. Although the marriages were arranged at those times, woman of her social status could choose someone who would be a worthy husband, and none of them deserved her.

To sum it up, suitors acted dishonorable in many different ways, abusing customs and laws of their (and our) times because they had physical and political power to back them up. Purpose of whole epos was to show what is proper behavior, and what is abominable to gods and punishable by death.

I ran this by my friend Matt Colvin, whose degree is in, and who teaches, classics. Here are his insights into the cultural context:

Mickey,

Missing from this discussion is the simultaneous second prong of the suitors’ strategy: namely, if they cannot make Penelope marry one of them, they can at least devour and waste so much of Odysseus’ household’s wealth as to diminish or cripple his family’s ability to contract and reinforce ties of xenia with other noble families in the Mycenaean world.

Also missing from that Stackexchange discussion is the function of Agamemnon as a mirror-story that contrasts with the central plot of the Odyssey. Agamemnon’s story comes up many times: Zeus’s first speech in Odyssey book 1 is a complaint about how Aegisthus, the successful seducer of Agamemnon’s wife Clytemnestra, has disobeyed the gods. Aegisthus is described with many of the same epithets and formulas as the suitors: both are “reckless” and disobey divine warnings against their attempted usurpation. Clytemnestra is herself the cousin of Penelope and both sister and sister-in-law of Helen of Troy, wife of Agamemnon’s brother Menelaus. Agamemnon is of course murdered by Aegisthus and Clytemnestra (Odysseus dialogues with his shade in Hades), and the suitors threaten to kill both Telemachus and Odysseus himself should he show up. Finally, Agamemnon’s son Orestes is held up many times as a model for Telemachus to emulate.

The fragility of noble power in Homeric society is also evidenced by the words that King Priam speaks to Achilles when he comes to his tent to ransom the body of Hector:

"Remember your own father, great godlike Achilles-
as old as I am, past the threshold of deadly old age!
No doubt the countrymen round about him plague him now, 
with no one there to defend him, beat away disaster.
No one — but at least he hears you're still alive
and his old heart rejoices, hopes rising, day by day,
to see his beloved son come sailing home from Troy.” (Iliad 24.483-489)

Telemachus’ inability to use force to evict the suitors from his house makes clear that their continued feasting is not merely bad etiquette, but a political power play in a society where wealth and hospitality were the means by which the noble families maintained their power — and where insufficient wealth or strength could spell overthrow by rival families. That Agamemnon was murdered and that Achilles’ father was presumed to face “disaster” without his strong son there to “beat away disaster” suggests that this sort of fragility was not unusual in the society that produced the Homeric epics.