Confounding versus endogenous variables. What is their relative hierarchical position?
The question is not totally clear, but I will attempt to give you some guidance. 

To answer your first questions, confounding variables are not a type of endogenous variable. We do not observe nor are we interested in the confounding variables, which means they are not endogenous variables in our model.

You later give the correct definition of an endogenous variable "An explanatory variable in a multiple regression model that is correlated with the error term". Hence, there can be several reasons why a variable would be endogenous, but they all have to do with correlation with the error term.

An endogenous variable is one, which cannot have a causal interpretation in a regression model. When something leads to a variable being endogenous, we call this a source of endogeneity.

As you mention, an important source of endogeneity are omitted variables. If we omit a variable, which affects the outcome variable, then the omitted variable is captured by the error term in our model. If the omitted variable is correlated with an explanatory variable, then that explanatory variable becomes endogenous, because it is now correlated with the error term.

Other important sources of endogeneity are reverse causality and simultaneity, as you mention. For reverse causality, we have that the explanatory variabe is supposed to influence the outcome variable, but if the outcome variable also affects the explanatory variable, then in our regression model, this latter channel is necessarily captured by the error term. This is because such a channel determines the relationship between the outcome and explanatory variable, but we cannot capture it in any variable. Putting the explanatory variable on the left side instead and using the outcome variable as an explanatory variable does not help either, because we then have the same problem. Then the explanatory variable is correlated with the error term, which makes the explanatory variable endogenous.

So overlapping features are that all sources of endogeneity stem from a correlation of an explanatory variable with the error term. Distinctions are the source of this correlation and consequently how to deal with it. For example, omitted variable bias may be dealt with by observing and adding the omitted variable to the regression. This strategy does not work when trying to address reverse causality.