And if you want to post a message - you should be able to click on the RED BUTTON and the top left of the page called "New Topic"
You should be able to see this regardless of whether you have joined the group.
It should ask you to join once you click on this.
If you can't see the button try to join the group first.
(The reason for the inconsistencies in your google group experience will be due to differences between different browsers)