Sounds like a fun project. Here’s a quick stab:
The “Lookup Helper” column is so that you can search for people by skill and by name. And the bracketed number is the count of active projects to which a person belongs—could help from over-assigning. Also, instead of directly joining People and Projects you could also create an Assignments table with a Projects and People column.
Yes. I assumed that if a project had “required skills” and people have “acquired skills” then they should pull from the same table so that it’s easier to search/match people to projects. Also it becomes easy to see which skills have NO people (or too many people) and which skills have the most projects, etc.