2. On GSoC GitHub page, there are 4 projects on Boost.Geometry, but are only 2 potential mentors. I guess that only 2 students are chosen, right? I just want to make sure.
I do not see how this affects the student's proposal but depending on the quality of the applications the number of selected students for Boost Geometry will be from zero to two.
Knowing how many spot are considered may help students to decide how much effort to put in secondary applications. Google allows to apply to more than one project/org at this stage. In general, I would advice to make most the effort in the main proposal of what you want to work, but still have backup proposals to submit. The main point of GSOC is helping integrate students as new members of the community while working in something cool, and many times great students with great proposals doesn't participate just because they put all eggs in a single basket that many others also put eggs and that basket only had space for 1/2 eggs. The GSOC goal can be achieved working in different libraries or even in different orgs than you preferred one, and the learning could be applied to work in your favourite project afterward if you didn't get it to happen on during the GSOC. BTW, if you apply to 2 project under same org, make clear what is your preference order.