Regarding the classic test pattern of Arrange-Act-Assert, I frequently find myself adding a counter-assertion that precedes Act. This way I know that the passing assertion
Depends on your testing environment/language, but usually if something in the Arrange part fails, an exception is thrown and the test fails displaying it instead of starting the Act part. So no, I usually don't use a second Assert part.
Also, in the case that your Arrange part is quite complex and doesn't always throw an exception, you might perhaps consider wrapping it inside some method and writing an own test for it, so you can be sure it won't fail (without throwing an exception).