Centre of Gravity
If the Moon was closer, the COG would have been nearer the centre of the Earth.
The COG will only emerge above Earth's surface when the ratio of the Moon's orbit radius to Earth's radius exceeds the ratio of Masses.
Mass ratio is 1:81
Current radius ratio is 1:15.9
Therefore the Moon needs to retreat to ~ 2,035,000 km (5 times its present distance), before the barycentre is outside the body of the Earth.
As for your other questions, you can tackle the specifics of each situation yourself - Masses of most bodies are available on Bill Arnett's Nine Planets.
I don't think the individual masses of Pluto and Charon are well enough characterised to go into much detail there.