The person above has wonderfully summed up the first and third questions so I shall attempt to further elaborate the second.

Well to understand this first lets establish some ground rules about socialism. Basically in socialism some private ownership is allowed. Like I have said before it is meant to be a transitory phase between capitalism and communism where the government is trying to redistribute all property. Socialist policies can be implemented in both democratic and authoritarian countries. Also note here that there are a LOT of socialist ideologies some of them don't even want communism like Democratic socialism. Some of the Nordic countries like Sweden and Denmark have their own Social Democratic Party which do come in and out of power. These countries are the best in the world especially by a human development Index so they must be doing something right and this negates the old capitalistic slogan that there is something intrinsically wrong with Socialism.

So lets say that for a country to be socialist it must have two basic properties: Central very powerful government that has goals of public welfare, re-distribution of property to make society more equitable.

Now let's return to the original question; is China Socialist? China likes to call itself "Socialist with Chinese characteristics." what that essentially means is that they have deviated a lot from the original Marx ideology (It is interesting to note here that for Karl Marx Socialism and Communism meant the same thing. He never introduced a "transitory" phase). Of the two properties mentioned above China definitely has the first. What about the second? Deng Xiaoping once said, "Under socialism, there can also be a market economy." That was the way he adopted the system and introduced a lot of incentives and economic reforms to promote free enterprise. China today has a large booming Private Sector which accounts for more than half of the whole Economy and employs the majority of the labour.

Now this may seem directly against the basic socialist ideals. Market economy is what Marx was against. Free enterprises had no place in communism. But if we look closer, Chinese government does in fact control all the factors of production. All land in China is state owned and they lease it out to people. People still own their own labour but the Chinese government has grand development plans which allocate certain amount of people to each sector for sustainable growth. Next comes capital, all banks in China are state run so they full control over that. Last factor is entrepreneurship. According to the Fortune Global 500 List, the top 15 Chinese companies with the biggest revenues are all state-owned and even the private owned companies must follow the large strategic goal frameworks of the government. So with a strong hand in all economic productive factors, China can be classified as a Socialist country.

I want to draw attention to the second basic property we had established-re-distribution of property to make society more equitable. China despite is motives isn't a very equitable society (yet). The classes still exist and there is evidence to show that the gap is growing. In fact they have the most inequality among the big economies with 30 million people living below the national poverty line yet a large number of billionaires. The government is also not very good with providing basic public services. Many Chinese often struggle to afford education and healthcare. So China has not been very successful with redistributing resources and hence doesn't fulfill one of the properties of socialism.

In conclusion, whether china is or is not socialist is up for debate since, like any ideology, socialism means many different things to many people.