Yes government can kill bitcoin in the way how they want to do it for example if there no more people who are appreciating bitcoin they can kill it easily
Bitcoins are not easily killed by the government. The government does not control bitcoin. If you want to kill bitcoin, all countries in the world must simultaneously block bitcoin. But I think this is totally unlikely
The bitcoin itself will no longer be killed by government. As long as the government has no access on the server of it, They will not control the bitcoin and it will still exists. Bitcoin is still in the market if the server will still have no plan in deletion of bitcoin. And i think, Bitcoin will exist forever.