Hello! Nice to meet you! First of all I want to say that you English is very good! I play in both Japan and North America so I can give my own experience.

3滅解散 (Three wipeouts and it's over.)
Sometimes you will see this in party finder especially on the last fight of a tier (4層) for example "3 wipe = disband" but often someone will just leave the party after anywhere between 1 wipe and 5 wipes. So it's sometimes difficult to get a learning party (練習PT) going for a long time.

【周回】(Three wipeouts and it's over) There is no rules and people may leave after 1 clear if they feel like it.

【取り抜け】 This is impossible in NA, and will never happen in party finder ever.
In North America there is only フリロ (free roll)

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North American servers tend to be "free-for-all" where people just do what they want.
There is no agreed upon rules and even if you write something in party finder (PT募集) people will just do as they please anyway.

Also because 周回 gets translated as "Loot" in the English settings, you'll see 周回 parties for many things other than "farming" (like weekly clear of savage fights for example)

Also, you will often see static parties (固定PT) with very little rules written down. Unlike in Japan where recruitments posts are very explicit in North America the recruitment may list only the desired role, schedule time, and ask for "prior raid experience" and that's all.