Hi Shankar,
1) You can achieve this by using a repeater with custom query where you will list the forum groups and create the links to appropriate forums. Another option is to place each group on separate document in the content tree and then list these pages in a menu or repeater.
2) This is matter of the CSS styles you are using, they are different for live site and for the edit mode in Tools section - in this section it is only a simple preview without heavy styling.
3)
a. This is achieved by CSS styles for forums, in this case it should be ForumImageDefault CSS
b. These links are displayed to authorized users. You can lock the forum so the users cannot add or reply to posts. Sticking the forum means that you can move up and down the sticked forums
c. Again, this can be achieved by CSS
4 and 5) You can use the Forum posts datasource web part to achieve this. You will need to pass the user ID to the data source and filter out the records.
Last one - this can be achieved by customizing the
forum design.