Is “harebrain” used commonly as a verb or adjective?

Harebrained is more often written as hare-brained, which makes it clearer that it doesn’t come from a root *harebrain, but is analogous to compounds like red-haired, duck-billed, flat-topped and so on.

So, it’s describing what kind of brain someone has: the brain of a hare, a proverbially daft, silly, jumpy animal. Or, by extension, it describes something that a hare-brained person might think up, or do, or support. A more common approximate synonym would be idiotic.

Hare-brained scheme in particular has become almost a cliché. Your example is very similar: “The agreement […] is hare-brained,” is saying it’s a stupid, idiotic idea.

It's an adjective, modifying "agreement." More commonly, though, it's used in a phrase such as "a harebrained idea."

The meaning, as you've probably gathered from that list of synonyms, is something like "ridiculous" or "nonsensical." So the editorialist is saying that it's a dumb idea.

The reason is that hares (ie turbocharged Rabbits) run around in the spring mating season, fighting with each other and generally behaving in an undignified manner.

So "mad as a march hare", "haring around", "harebrained" all mean something like frivolous, un-focussed, scatterbrained etc rather than directly stupid.

Harebrained is an adjective, often describing ideas/schemes/plans that are at least slightly, if not completely, crazy.

I've never heard of the word "harebrain", whether a verb or something else.