Communism is democratic, yes. This can have multiple parties (which is in practice in several AES states), but generally having different parties is not the same as having democratic control. It's arguably more important to be able to vote on what you want, or who you want to do it, within an existing party or party-less system. As an example, among a local council, rather than voting on a party, it makes more sense to vote on which representative from said council will participate in the regional council, not necessarily which party.
Secondly, again, you are confusing a "State" in the Marxist sense, ie the elements of government that denote class distinctions (private property rights, as an example) with the colloquial sense of the word "State," which is largely synonymous with government. Communism would have a government, complete with elections and representatives, without a state, hence me bolding Engels when he says "The government of persons is replaced by the administration of things and the direction of the processes of production." You cannot direct the processes of production without, you know, directing production.
Moreover, corruption likely will never fully go away, but it will be minimized over time, certainly in comparison to modern Capitalism, and even early Socialism. Communism isn't some Utopia free from any worry or problem, and Marxists are the first to point this out. It's usually non-Marxists that pretend Communism is supposed to be perfect and thus impossible, actually.