Of course they are, subsidies are one of capital's favourite methods to siphon money out of the populace. Or were you under the impression that greedy people like playing fair on fair markets?
Yes, and the EU largely responds in the sectors of US subsidy. Food imports are restricted. Airbus and Boeing are constant sources of trade spats, etc.
Chinese subsidy makes American subsidy look like childs play. Their response to China should match that discrepancy.
It's not that simple. Caricatures are easy, but the fact remains that the Chinese auto makers are heavily subsidized and it's that government support that allows them (partially at least) to undercut the European auto makers.
That being said, the European auto makers really deserve to be hurt for their arrogance. And that's coming from someone whose income is directly related to how well they do.
They're fighting Chinese market manipulation that is specifically designed to make the world dependent on them and lowers wages across the world by creating massive market imbalances. Every nation with two brain cells should ban the import of all Chinese vehicles and eventually all Chinese industry entirely.
Chinese electric car makers get absolutely massive state subsidies. There are companies like Nio that have never made a single dollar of profit. Nio has been losing money on every single car they sell, to the point where they've been losing almost a billion dollars in the last quarter alone.
However, China doesn't care. The state keeps financing these companies, because if they can undermine European and American auto makers to the point where they're simply unable to compete and maybe even completely collapse, then Chinese car makers will be the only ones left in the market, and they'll be able to charge any price they want.
And realistically, which American or European car maker will be able to compete with a multitude of Chinese competitors that all can afford to lose billions and billions every year without batting an eye?