For the first one, it all depends on what permissions you want the users to have in the project area and various team areas. Do you want everybody to do things at the project area and only a selected few to do things in a particular team area, or everybody to do things in the team area only with only few of them to do things at the project area? Note that the project area and team areas can have different roles and permissions. If a user does not appear in a project area or team area, he should have the "Everybody" role.

For the second one, I expect the same.

If I'm not mistaken, unless you share your query in a team/project area, or particular user(s) (in the Details tab), the query is "private". If it's shared, others can see it in the Shared Queries folder. Public Shared Queries can only be configured in the process configuration, which means that only an administrator can do it.