Is the Moon the same shape when seen from different places on Earth?
Yes. At the same moment, the Moon looks pretty much the same shape, if you can see it, wherever you are on Earth. The difference made by travelling a few thousand miles to the other side of the world is very slight because the Moon is dozens of times further away than that. It doesn’t necessarily look the ‘same way up’, though. Its orientation, in a different observer’s sky, will probably be different – but if it’s visible, it will be the same shape. So, Full Moon happens at the same moment everywhere on Earth – although of course the time shown on local clocks will depend on the time-zone to which they are set.