One could argue that cooperatives are not private ownership, but that would be futile. Such an argument would mean that owning stock could also not be private ownership.
Worker cooperatives are in effect private ownership as they belong to the members of the cooperative. They are closer to capitalism than to socialism because in a pure socialist world everything would be needed to be controlled by the government. A pure socialist world could not allow for cooperatives to exist as they are a step in the direction of capitalism.
The model is thus closer to capitalism as there are no rules that prohibit cooperatives from making revenue and that revenue increases the capital stock which in turn belongs to the members of the cooperative (or the stock holders). A cooperative is thus only a simpler form of a stock company.
Still mostly socialist parties promote this form of ownership as they see it as a first step of giving up parts of control over a company from a simple board to a wider population of members. Yet as has been shown above this is simply a question about how a company or a cooperative is governed and not about whom it belongs to.
Regarding the bonus question, I can't tell and a quick google search did not turn anything up either.