bitcoin is not a company that can be put out of business
Yes, but the exchanges, which are an integral part of the Bitcoin economy can be.
Depends on the country. Russian sites for one, are notorious for hanging around for years.
Only political favours or large payoffs from other countries will make the russian authorities give a shit about sites hosted in their country, legal or not
(And BTC exchanges are currently legal).
Many 'grey area' sites pay money to cops in these kind of nations so there is low incentive for interception