Will there be a typewriter mode? (center text vertically, focus on active line)
What is your definition of “typewriter mode”? If it is “plain text” without stylistic decoration, it is better to use a text editor like KWritre, gedit or notepad.
Will there be a typewriter mode?
There is already - you just have to set it up. Alternatively, just use Notepad.
1 Go Tools > AutoCorrect Options …, and stop all the automatic stuff.
2 Delete all the unwanted styles for paragraph, character, frame, page and lists. Set the default font to Courier 12 point normal. Save it as your default template.
3 Switch on Direct cursor in Tools > Options …, so you can click anywhere in a page and start typing there.
4 Go Tools > Options …, and disable anything you don’t like
Voila! You have set up LO as a typewriter.
centre text vertically
Place the text in a Frame and centre the Frame vertically on the page.
focus on active line
Focus is where the cursor is. Find the cursor …
The closest you can get to “center text vertically, focus on active line” is the full screen mode: View → Full screen or Ctrl Shift J. I know, it is not the same, but it is something 
There will not be, unless someone makes it.
I didn’t research on purpose, but your question is the first I came across asking about such a feature. It should not have a huge user base. Also, while it might be convenient for some people, for most of them the only purpose is to avoid learning something new; and by that, maybe misusing the software which purpose is creating electronic documents as something different. So, while you may use such a software for different purposes, I suppose that creating UI that encourages such misuse is not a good thing.
Seeing just one line of the text… cursor being always in same place, and text moving as you type… Anti-pattern. Makes it difficult to see the context; each time I want to look at some words in previous sentences, I must search them in different place on screen; creates unwanted image flicker, motion and jumps (when line wraps)… And fatigue because of static head position; is this anti-pattern targeted at avoiding movements by eyes, and neck, which (movements) may be beneficial for health?
But as I said, it awaits its developer. So, you may step in and develop it, and suggest your creation for inclusion into LO.