If you don't want anybody send invitation to become member of groups in career, projects or services site, visit the my account page. Click edit, set allow invitation choice as needed and save.

To set your profiles to public/private visit the profiles site. In the rightside user menu click on profile privacy link. Set the privacy level as you wish.
If you set your profiles to public it doesn't mean that all the profiles will be public.

Visit manage profiles and click the link manage profiles in the right side user menu.
The 'about me' profiles can be set to private or public by editing them. In the edit page for each profile, you can see the profile privacy checkbox at the bottom to choose.

Please go to the research website. If you are professional who has permission to create report forms for various services, on the right side you can see your content page. Go to your content page. On the page you can browse the contents you have created including report forms. You can create report forms or edit the report forms you created.

Go to the projects home page. On the right-side menu click on your groups. It will list all your groups including projects, your relationship group, and the relationship groups of others in which you are a member.