- Can the plugin be MIT instead of GPL3?
Yes. Plugins for GPL applications can be under any GPL-compatible license, assuming the interaction between the application and the plugin is such that the GPL terms apply also to the plugin.
The GPL license requires that the combination of application+plugin is distributed under the GPL terms, but that does not mean that each separately identifiable part of that combination must also be licensed under the GPL when those parts are separated. The same mechanism is in effect here that allows you to use non-GPL libraries in a GPL application.
- Can Charlie (the copyright owner of the plugin) "mutate" the license back-and-forth from GPL3 to MIT or from MIT to GPL3 if the author specified X license?
- Could the plugin be releaded under the GNU All-Permissive license?
- Can Charlie, the copyright owner "move" its software from All-Permissive to MIT or GPL3?
Yes to all of them. As copyright holder, Charlie has (gained) the right to set the copyright license and to change it at whim. Charlie can even put a proprietary, GPL-incompatible, license on the plugin, but that would prevent Charlie from distributing the plugin.
Is there any public matrix of "from" to "to" possibilities in an easy way to understand?
Actually changing a license can only be done by or with express permission of all copyright holders. In that case, everything is possible.
For using the work from others in an application (either as a library or by copying), you need to have a copyright license. This license can put restrictions on what you are allowed to do, like a requirement to make the source code public under an open-source license.
Two licenses are incompatible with each other if they have requirements that cannot be both fulfilled at the same time. The problem here is that you are only allowed to distribute your application if you can fulfill all the requirements from all applicable licenses at the same time. If you can't, for example due to contradictory requirements, then you are not allowed to distribute.
There is a chart about license compatibility in the Wikipedia article on the topic.