Although I'm not using TGUI, I'll still give you my feedback. I mean the questions aren't that specific to TGUI.
This means that you can use the tab key to focus another object. Is this really necessary?
I think this depends heavily on the use cases of TGUI. For GUI applications, removing that feature would be a big no-go. Take for example a login dialog with a username and a password text field and a button. Would you really like to select the first text field, enter the name, then grab the mouse again, then enter the password, grab the mouse again and click 'login', or wouldn't you much rather, enter name, tab, enter password, tab, enter?
On the other hand, when you use TGUI for a game I guess it wouldn't really matter, since you most probably will have your mouse in your hand anyways, then again there could still be some use cases.
My opionion: Don't remove it!
but it will also open other possibilities (e.g. adding a tab character in a text box).
I'm not sure how you handel textboxes at the moment, but normally for GUIs one makes a difference between textarea boxes with multiple lines and a one liner textbox. For a one liner textbox it usually doesn't make sense to allow tabs (tabs are there for formatting, what would one want to format in one line) but they can make sense in a textarea. Now there are diffrent situations where one wants to allow tabs in textarea fields and one maybe doesn't, so a switch that lets the programmer use tab in one or the other way would kind of solve that problem.
Secondly, something has to happen with selecting text in edit boxes and text boxes. Currently you can have text selected in multiple edit boxes at the same time. This shouldn't be to hard to solve, but it brings up a question. Is it necessary that when you click outside the edit box, the text stays selected? Currently the text will get deselected anyway when clicking back into the edit box. It would even save another color if it would get deselected right away when clicking on another object.
Both possibilites exist in other GUIs, so I guess it also depends a bit on the kind of application. If you make something in the direction of a text editor losing the selection can be quite annoying, for other uses IMHO it doesn't really matter. Since the selection gets lost anyway I'd say you can automatically deselect it (or does it stay selected when 'tabbing' the the textbox?