Never reach out to a mentor via LinkedIn when trying to ask questions about a GSoC idea, that is not acceptable and will likely be ignored by the mentor and will leave them with a poor impression of you.
Reach out to the organization via their preferred contact methods that they list on their page on the GSoC site. If they have a 'Contributor Guidance' section on their GSoC page (at the bottom of the screen) then they will tell you exactly how they want to be contacted.