On an ice is the text: "The Runner can spend a click to break any subroutine ...".

Does this mean that the corp-player dont need an icebreaker when he uses clicks?

Or must the corp-player use an icebreaker and need a strength from 6?

I assume you mean 'runner' in those last two sentences instead of 'corp-player'. Anyhow, the runner does not need an icebreaker to use the ability on bioroid ice (such as Heimdall 1.0 ) -- it's an ability on the ice itself.

If using clicks to break subroutines on a Bioroid, no icebreaker is needed.