TS,
Yes no change to the gearing ratio / LVR.
I think YES to the second question, depending on who's debt it is.
But in principle buying your own debt back at a lower rate would obviously improve your LVR if you had the spare cash. Otherwise you would need to run a capital raising which would dilute the capital base.
You could argue forever if this is a good or bad thing......
Leave that to others to run.