You can make each one of your pictures private or public. That way your profile will always be public and some or all of your picutres can be hidden if you wish them to be.
You can delete your picture by clicking the 3 dots on the right side above the picture, an option 'delete a picture' should appear. After clicking the option and confirming, the picture will be deleted from your profile.
After finishing an activity there is an option to post a picture, which we highly encourage as it helps you become part of the community and for future rewards that we are preparing for you ;)