There's a lot going on in your questions with regards to different types of insurance involved in the space business. As Lar pointed out, you can get insurance for pretty much any perceived business risk, provided you are willing to pay enough.
There are instances in the space business where insurance is
required - particularly with regards to 3rd party damages resulting from launches. It gets complicated quick.
When it comes to liability - the international legal regime is guided by the U.N.'s "Convention on International Liability for Damage Caused by Space Objects" - which generally places the liability on the launching state:
http://www.unoosa.org/oosa/en/ourwork/spacelaw/treaties/liability-convention.html. That principle, which basically flows down from the outer space treaty, is an important driver for why countries establish oversight/licensing regimes for launches from their territory.
Each space fairing country creates its own regime for how it deals with space launch liability, but nearly all launching countries provide some sort of government backstop ("indemnification") to the launch companies' liability for 3rd party losses, even for non-governmental ("commercial") launches.
In the U.S., in order to obtain a commercial launch license a company is required to purchase insurance or "demonstrate financial responsibility" (in other words, set a bunch of money aside) for 3rd party damages up to the amount the FAA determines to be the "maximum probably loss." My understanding is that typical MPL's for large commercial launches are often in the tens of millions of dollars, and the insurance generally costs something on the order of 10% of the coverage. So for a ~$100 million launch with an MPL of $40 million, the 3rd party liability insurance might be a few million dollars. The trajectory, explosive potential for the rocket, reliability, etc all factor into the price. A small, highly reliable rocket launching from a very remote location that doesn't really overfly anything would be much cheaper than a large, unproved rocket that launches from/over (or returns to) a relatively populated area.
Above the MPL amount, the U.S. government indemnifies the launch provider up to a certain limit specified in law. I think it's around $1-2 Billion or so. Then for any losses above that limit the company is back on the hook. The "catch" is that the U.S. government's responsibility is only to the extent Congress appropriates the money following a loss. This GAO report discusses the U.S. indemnification and launch insurance regime in some detail:
https://www.gao.gov/assets/670/660635.pdf And this posting by former FAA attorney Laura Montgomery provides some commentary:
http://groundbasedspacematters.com/index.php/2018/06/19/u-s-space-launch-and-reentry-indemnification/