In the event recent tensions between Armenia and Azerbaijan grow into all out war, will Russia use the conflict as a way of increasing its control and power (directly or indirectly) in a the Caucasus?
To the extent that they can. Their ability to influence is waning due to their economic decline. They're beginning to tax new oil explorations, something that's regarded as the cannibalization of their oil industry. That doesn't mean that they won't continue to seek to control events outside their borders, but their capacity to do so is diminishing by the day.