Scientists today, are they too focused on themselves and their own domains, or is the opposite true?
Lots of variation! Focus is crucial for most kinds of scholarship. Specialization demands a narrowing of focus, not on the narcissistic self but on the unselfish working self. That intense focus separates the more from the less successful scholars, more than sheer ability.
 
How can scientists offer an anti-dote to various forms of fake news in the so-called post-truth era?
Analyze communication as it involves perception, rhetoric, & propaganda, be aware of the fact vs. opinion distinction. You are entitled to your own opinions but not your own facts. Still be aware that the categories can change. Always ask, "Says who?" and based on what empirical, logical or value standards.
 
How can scientists increase their impact on society?
Should they all? There is a danger of rule by technocrats, Plato notwithstanding. As the Americans say, " Different strokes for different folks". We need a division of labor. This should depend on the topic, sponsor, and perhaps the life cycle of the scholar. There is a good reason why universities were set apart from society. Independence & unfettered freedom of thought are vital for truths, whether scientific or ethical.
 
What should be the role of universities in today's world?
Wow! I need at least a semester for that one. There are many answers. A good one for now "Speak truth to power ". When appropriate introduce doubt but do so with humility since things can change. Be ready to doubt your doubts.
 
There are many developments that can be construed as threatening: climate change, job destruction by automatisation, loss of privacy through big data enterprises... Which current developments pose the greatest threat in your opinion?
A few more threatening developments: nuclear and other emerging forms of destruction, science & technology developments not guided by ethics & public discussion, and a world further driven not by the harsh, coercive forms of social control noted by Orwell, but by the soft manipulative, seductive & invisible forms identified by Huxley.