How important is core training for 400m runners?

how much time or days per week shall i do core work?
Is it really that important to train?

You can train your core daily if you want - reps - not heavy.
check out the GPP dvd for practical demo’s

You don’t have to do any specific training you don’t want too - nobody is forcing you.
But, for somebody with a history of injuries - you need to figure out what you want.

1 - just to run
or
2 - to run pain free, to best of your ability
or
just to run pain free

Those are your three options.

I guess what you are saying is that to both stay injury free and reach my potetial I should do some core training?

Yes - and a lot more work.
You need to get strong - not like a bodybuilder though.
You need power - plyro’s can help here as with the running
You need flexibility
You need to keep your muscle loose from knotts - therapy
You need good nutrition
You need great posture - esp hips

There is a lot to work on. Don’t do certain things at your own risk.

Sprinting - or running in generally, is a lot harder than simply, run fast, turn left. I wish it was that easy.