Both of these are actually idiomatic abbreviations for common expressions.
With the first example: "As necessary" is an abbreviation for "as is necessary (to achieve some result)". Examples:
After running the race, make sure you drink as much water as (is) necessary (for you to feel fully recovered).
Before you turn in your assignment, be sure to check it for completeness and accuracy. Take as much time as (is) necessary (to ensure there are no mistakes).
With the second example: There is a common grammatical structure that may be familiar to you, "as X as Y", used to relate something to something else, for example
She is as smart as a computer
This is commonly used to relate an adjective to an opinion:
The question isn't as difficult as you might think.
Your second example uses an abbreviated form of this structure. As written the sentence is incomplete, and not grammatical, but nevertheless it would be commonly interpreted to mean something like:
It's not really as serious (as you might expect).
Again, in both these cases the missing parts should be easily understood from context.