You can certainly do regression with multiple dependent variables - this is referred to as canonical correlation - but from a methodology standpoint, it would be easier to interpret the results if you did several separate multiple regressions, each with one dependent variable (or just a single multiple regression if you used a single index of political participation as the dependent variable).

If you go with one dichotomous dependent variable, this would be logistic regression (or discriminant analysis), and you would need a large sample size to detect significant relationships.

On the topic of indexes - are these indices something you've made up, or are they substantiated by prior published research? Be careful here - you'll need to justify how these indices are comprised...

- i.e., as the index "increases," you'll need to show that this indicates an increase in the measured "activity."

- you'll also need to show that the index is "sufficient" and/or "complete" - in other words does it adequately measure what you think it measures - prior published research would help here