Regarding your question about the full moon vs dark moon issue. Here are my personal views on it. Study it yourself though.
Some people use Psalms 81:3 to say that the moon needs to be full at the start of the month. I read it differently.
Blow the ram’s horn at the time of the New Moon, At the full moon, ON our festival/CHAG day.
In Exodus 12:6-12, Passover and the Feast of unleavened bread is spoken about. In verse 12 it speaks of the Festival (which the original word is CHAG as in Psalms 81:3)
Exo 12:6‘And you shall keep it until the fourteenth day of the same month.Then all the assembly of the congregation of Yisra’el shall kill it between the evenings.
Exo 12:7 ‘And they shall take some of the blood and put it on the two door posts and on the lintel of the houses where they eat it.
Exo 12:8 ‘And they shall eat the flesh on that night, roasted in fire – with unleavened bread and with bitter herbs they shall eat it.
Exo 12:9 ‘Do not eat it raw, nor boiled at all with water, but roasted in fire, its head with its legs and its inward parts.
Exo 12:10 ‘And do not leave of it until morning, and what remains of it until morning you are to burn with fire.
Exo 12:11 ‘And this is how you eat it: your loins girded,your sandals on your feet, and your staff in your hand. And you shall eat it in haste. It is the Passover of Yahuah.
Exo 12:12 ‘And I shall pass through the land of Mitsrayim on that night, and shall smite all the first-born in the land of Mitsrayim, both man and beast. And on all the mighty ones of Mitsrayim I shall execute judgment. I am Yahuah.
Exo 12:13 ‘And the blood shall be a sign for you on the houses where you are. And when I see the blood, I shall pass over you, and let the plague not come on you to destroy you when I smite the land of Mitsrayim.
Exo 12:14 ‘And this day shall become to you a remembrance. And you shall observe it as a festival/CHAG to Yahuah throughout your generations – observe it as a festival/CHAG, an everlasting law.
We know the 15th was a CHAG in the first month…..
‘And ON the fifteenth day of this month is the Festival/CHAG of Unleavened Bread to Yahuah – seven days you eat unleavened bread.
We know the 15th was a CHAG in the seventh month…..
Lev 23:34“Speak to the children of Yisra’el, saying, ‘On the fifteenth day of this seventh month is the Festival/CHAG of Booths for seven days to YHWH.
And when you view Psalms 81:3 again which says ” At the full moon, ON our festival/CHAG day.” the full moon needs to be seen upon the 15th of the month.
This is just my view on the subject. Others see differently the same way they see differently for the Sabbath day.