Should I use 'health check' or 'healthcheck'?
Solution 1:
You should use "health check". The compound word "healthcheck" is not common.
This compound word may sound more natural to you because there is a common compound word used in this setting with almost the same meaning: "checkup".
To see why "health check" is better, try replacing those two words with two words that have similar grammatical and semantic roles: "disk test". Would you say "I'm running a disktest"? I think not.