How do you weigh each one of those? What if a country is more transparent but also has more violence than another one?
Isn't that why we vote?
Not being able to define your interest can be due to lack of education, unwillingness to take part in the political process, etc.
Similarly, we've done a decent job of crushing political machines and corrupt unions... but a poor job of crushing the powerful business interests and anti-the-small-guy forces they (sometimes) effectively opposed. As a friend of mine put it, our system used to feature various kaiju fighting, all of them wrecking cities, but some of them doing so while trying to save us, some while trying to harm us. We eliminated all the kaiju that were working to save us (smashing a city block here and there and eating the occasional fire truck, sure) but didn't do anything about the ones trying to harm us, with predictable results.
Trust isn't everlasting, specially for a "person". I can put more of my trust in a "process" (e.g. democracy) and its continuous evolution towards betterment, than letting "someone else" make my decisions for me.
No, it's not.
But a democratic republic or representative democracy with republican form (as opposed to, e.g., a constitutional monarchy) is both a form of democracy and a form of republic.
There are autocratic and/or theocratic republics, among others, that are not forms of democracy.