I have created a couple of new projects (I am an admin) but they are not appearing once I am out of 'Administation' mode.
The default Project Lead is appearing in Red font for the projects in question.
Looks like you haven't se the project permissions correctly.
Assuming it is JIRA, here is the documentation.
https://confluence.atlassian.com/display/JIRA/Managing+Project+Permissions
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