When I am programming in Eclipse, the auto-complete \ suggestions box usually opens when typing a dot (for example after typing
public String toString()
FYI, in Eclipse terminology this feature is called Content Assist.
Is there any way to make the suggestions box visible all the time, showing suggestions in real-time (and showing a blank box when there are no available suggestions) ?
No, that's not possible. You can invoke it any time you want via Ctrl+Space (Command+Space on Mac)
Is there any way to add permanent custom suggestions to the suggestions box (e.g. a switch case template or a line of code like public String toString()) ?
Yes, you can add your own templates via Preferences > Java > Editor > Templates
Is there any way to re-order the suggestions box (e.g. class private variables before general functions or System.out.println() before System.out.print()) ?
Not really. There is some control of the order for "cycling" through proposal types via Preferences > Java > Content Assist > Advanced, but it's not really what you're looking for. The order of proposals is, I think, based on the current context of when Content Assist is invoked.
Is there any way to re-design the suggestions box - i.e changing its text color, background color, re-sizing the suggestions box window and removing the yellow java-doc pop-up?
All of the customization option are available under Preferences > Java > Content Assist; color options are available under Preferences > General > Appearance > Color and Fonts, but I think the colors for that pop-up might come from your operating system color settings.
If you're using (or willing to use) Eclipse Juno (4.2) then there is a new project call Code Recommenders that you might find interesting.