1. The other parts of the project can remain MIT or any other gpl compatible license. A condition for distributing the GPL library is that the whole project get covered by the GPL. A way to look at this is to think of parts only having to follow their own license, while the combined work has to follow all licenses that has clauses for combined works. In practice this mean that for example the GPL patent clause will cover the whole project and not only the library.

2. As each part has it own license you can mix and match how ever you want as long as the combined parts are compatible. If you are the author of all the project code (other than the CGAL library) then you have additional rights to change the license of future version, but in this case it is unlikely to matter as MIT is very permissive license. As the copyright author, the only way to "lose control" is that you can't retroactive change licenses of past publications of old version. New publications and new version however is fully within the control of the copyright author.

3. Plugins live in a grey area of copyright. From what I have seen the most common answer is that they are not covered by the license of the main program. Different organization makes different interpretation here, and for what it is worth FSF has published where they will enforce GPL (https://www.gnu.org/licenses/gpl-faq.html#GPLPlugins). I think Linux foundation determine the line based on GPL_ONLY flag in the kernel code, and wordpress has it own interpretation. I would however say that it is a bit of a stretch for a library authors to complain about the plugins licenses to software which uses the library unless there is very heavy and obvious 1:1 link between the plugin API and the library.