I would use "επείγουσα ανάγκη" for "emergency," and "need" for "ανάγκη." I also find the original sentence somewhat unnatural. "Υπάρχει ανάγκη" might work better.
This is a very common and natural way to talk about an emergency. It's an idiom. Maybe some people also say "υπάρχει ανάγκη" but I haven't heard it. "Υπάρχει μια ανάγκη" - There's a need/necessity
Can this also be translated to "it is necessary" as my German-Greek dictionary and wordreference.com claim?
Yeah, but this is the medical skills section. If you needed help and shouted "it is necessary", you wouldn't get it.
Can you also say, "Είναι επείγον!"?
what about "It is a need"?