About Credit and Debt?

Hello guys,

My second question on this forum . The more I try to figure out how our financial institutions work, the more the story becomes fascinating to me.

So I have the following questions now:
a) Is every government in the world under debt? (i heard that debt and credit are 'basic' feature of our economy)
b) Can governments reverse the process and opt not being in debt? (will it be good or bad for the system?)
c) If debt is Okay then why is Greece's debt bad? Can't the government issue treasure bonds and let the central bank print more currency in return? Is that already happening? What effect this has or will have in the purchasing power or value of Euro?
d) Is hyperinflation imminent? Is it bound to plague every economy eventually because of our debt based system?

Thank you all for your encouraging replies