The WP User Frontend plugin will meet all your needs. You can find the plugin here: https://wordpress.org/extend/plugins/wp-user-frontend/.
The plugin gives ability to the user to create new post, edit post, edit profile from site frontend. So users doesn’t need to enter the admin panel. Everything they need to do can be done from the frontend.
If you do a small Google search you will encounter many other plugins with similair feautures. I do believe the WP User Frontend will be most compatibible with your needs and wants.