1. conjecture, slanted ¶
People made conjectured this slanted pyramids from all aspectss about why the sides of these pyramids were slanted.

Not clear what you mean. A conjecture is a theory, to make a conjecture is to suggest a theory. You can use it as a verb but the verb often wants a clause explaining what the conjecture is.

"He conjectured that the pyramid was unfinished."

Slanted: an adjective that means the thing leans at an angle (like the sides of a pyramid, yes) or past tense of the verb "to slant", which means "to be slanted; to lean to one side". "The wall had begun to slant."

I'm curious why you chose to use "aspects" here? It's possibly a misunderstanding.

Most of them agreed that these pyramids were in an unfinished state.

More natural: "were unfinished."

2.outright, adversarial ¶
In the past, the Liberty thought theat poverty would do harm to the children, while the welfare would benefit the children.

Unclear what "the Liberty" is. I interpret it as a group, like a political party or a charity, whose name is "Liberty".

These "the"s make it sound like you're talking about specific children, a specific instance of poverty, a specific welfare program. Like:

"They thought that the poverty in this city would do harm to the children living there, while the welfare program they supported would benefit these children."

Thus they held outright adversarial opinions on the measures that were taken to reduce people's reliance on welfare.

"Outright adversarial" is used exactly right here.

They are a group of people, so strictly speaking they hold opinions. Each person in the group holds an opinion. But it's common to treat a group like this as if it's singular - "they held an outright adversarial opinion".