In the US, I'd say to 'argue against' rather than 'argue down,' but it would have the same meaning: they are arguing against the proposal, i.e. not in favor of the proposal, advocating against the details of the proposal, etc.

It's hard to say for certain without context. I think it means they tried to defeat the proposal by making arguments against it.

Thumbs down! They expressed opposition.

This could be used in describing a formal meeting in which a group of people debates a series of items and then takes votes for and against them. The phrasal verb "argue down" combines two ideas in a straightforward say. To "argue" means "to debate," to give reasons in favor or against some proposal. To "argue DOWN" makes it clear that the speakers are AGAINST the proposal. It also carries the idea that they wanted to end or finish the argument. They wanted to win the debate. They want the debate to end, finally, with the meeting rejecting the proposal--"voting it down"--and moving on to the next item in the agenda. "Down" is one of those short words with dozens of meanings. The simplest meaning of "down" is a direction--the of "up." However, it can sometimes carry the meaning of "put an end to" or "stop." "The meeting voted down the proposal." "The speaker was shouted down by demonstrators." "A server problem put the website down."