Socialism is an umbrella term with a wide range of different sub-ideologies, and so the answers will be different for each question depending on the strand of socialism. The best I can do is give you some information regarding some basics and some of the different strands of thought.
Socialism is an economic system in which the means of production (factories, land, capital, etc) are democratically owned and controlled by the workers/the community, and used to produce goods and services for use, rather than for profit. Most, but not all, socialists don't advocate for markets, instead opting for a planned economy (either centralised or decentralised) or a gift economy.
The proletariat is the class of people who don't own the means of production and have to sell their labour to survive.
The bourgeoisie is the class of people who own the means of production and extracts surplus value from the labour done by the proletariat.
Communism is a stateless, classless, and moneyless society, in which the means of production are owned and controlled by the community, and the goal for most socialist ideologies.
There are generally two major splits in socialist ideologies. A split between Marxist forms of socialism and anarchism, and one between those who advocated reform and those who advocated revolution.
Marxist forms of socialism build on the theories of (surprise, surprise!) Karl Marx. Generally speaking, it advocates for workers to seize the state, and create a transitional state between capitalism and communism known as the dictatorship of the proletariat. Note that no socialist, including Marx himself, advocates that this state be an actual dictatorship - the term was a rough translation from the German used by Marx that stuck around, and essentially just means which class had the political power (ie, capitalism would be a dictatorship of the bourgeoisie), as Marx understood the state as essentially the result of class contradictions and used by the ruling class to repress class antagonisms and maintain the current system. He uses the example of the Paris Commune, a delegative democracy, as his model of the DotP.
Leninism is a Marxist form of socialism and advocates for vanguardism and democratic centralism.
Anarchism, while it can rely on Marxist analysis, does not inherently do so. It generally seeks to abolish all unjustified hierarchy, and sees both capitalism and the state as such. They see the state as the monopoly on the use of force and argue that the state can never be used for the interests of the workers, and must be abolished. This is because that the DotP will ultimately become a new bureaucratic class, a la the Soviet Union and the nomenklatura.
The Soviet Union received a lot of criticism from many Marxists as well, for this and/or other reasons.
Trotskyism and Left Communism both criticised the Soviet Union. Trotskyism criticises Stalin and generally identifies the Soviet Union as a "degenerated workers state", but builds on Leninism and advocates for concepts such as permanent revolution, the transitional programme, etc. Left Communism claims to be more authentically left, asserting that both Stalin AND Lenin made huge errors, the Soviet Union was "state-capitalist", and rejects vanguardism and democratic centralism.
Anarchism and Left Communism are sometimes identified as libertarian socialist, as opposed to ideologies that build on Leninism.
All of the above ideologies have historically rejected reformism, the idea that we can use the capitalist state and economic system to reform society to become socialist. However, this is not to say that they all reject reforms in general.
Democratic socialism is generally a nebulous term, generally argued by many on this subreddit to be a form of socialism that advocates reformism as a tactic. However, I would personally call such an ideology "reformist socialism".
Social democracy evolved out of this trend of reformist socialism, and essentially gave up on socialism altogether. Instead, it advocates for a strong welfare state with capitalism. As such, we generally don't consider social democracy to be a form of socialism. Examples include the Scandinavia countries, Bernie Sanders, etc.
I hope this answer helps you. :)