What is the significance to them of Paul saying that Christ is seated at God's right hand in the heavenly realms?
Christ is now placed above any realm or sphere which the gentile christians once knew demonstrating Gods supremacy causing the re-enforcement of their faith in God.
In what sense are these spirit beings and powers "under his feet"?
In the literal sense as being conquered, dethroned, stripped of any strong hold that they had on the minds of the Gentile christians before their conversion.