Two noob questions
(1) How do I get rid of (on the Web site) the big red arrow and the thing urging me to "Add your first project now"?
(2) What is the difference between using the standard Web UI and using the ToDoist applications for Chrome and Firefox?
Those types of messages will disappear when you complete the thing it's asking you to do, or when it's been clicked on. So when you create a project, that message will go away :)
The extensions for Chrome & Firefox are smaller versions of the web UI which can be accessed anywhere you are browsing. It's a button that you press that brings up an overlay or sidebar with Todoist inside. It makes it easy to access Todoist from anywhere you are on the web.
I don't want to start a project, how do I get rid of it?
Todoist only works with projects, a task needs to be part of a project. If you are referring to the Inbox, this can not be removed. Any other project, you can right click and delete.