Welcome here AlexDeK!
I may be missing what you want to do, but text justification is accessed through the Properties dialog. (F2) or Windows>Properties.
That dialog is so valuable that you should just keep it open all the time and maybe set it off to the right.
If you have a test frame open, select it and click on the "Text" tab in the Properties Dialog. You should see the font family name, the fint size, line spacing and then five buttons that look like pages of text (or 1.4.6, or 1.5.1 versions I have - yours should be similar if a different version.)
Those five buttons will affect changes in justification in your text frame.
For this demonstration - have a text frame with a couple of paragraphs of text within itm and before you follow further, please note that there are two levels of focus on a text frame.
The first that shows up if your focus was elsewhere and you click, once, within the text frame, will create a red line as the edge of the frame, and will have little red squares at the corners and centerpoints of the frame - will allow you to manipulate the frame as a whole.
The second kind of focus within the frame allows you to edit directly at the insertion point - the blinking line.
You want the first kind of focus. Click just once and verify that the red corner squares are telling you that you can adjust the whole frame.
Now - click on various of the five buttons I mentioned earlier, and you will get left justified, center, right, both sides, and both sides with the last line forced across the whole width. The last button I have not found a happy use for.
I am not sure what you mean by the "height" in "...full framing, height... " Can you elaborate and also tell me if my remarks so far are aimed at your question? Are you talking about resizing the height of the text frame to fit closely around the text? If so, those red squares in the frame outline when you are manipulating the entire frame can be used as handles to re-size the frame - in your case use the one at botton center by putting the mouse pointer over it and when the pointer turns into arrows you can click and drag the frame shape as wanted.
Did this make any sense?