How do insurance companies find out about existing health conditions?

I would suggest to come clean and risk the rejection.

I have a friend who has attemptedsuicide twice in her life. Without knowing that health related insurance would normally reject such cases, she was convince by P agent to buy health plan during road show 8 years ago. The policy was rejected and P agent did not even call to follow up until she was about to call for insurance coverage for day ward case.

She then spoke to a lot of agents from a lot of companies (including those extremely experienced ones), all verbally shared that she don't even need to try, it will be rejected. One agent even told her to not declare and take the risk. She rejected because the reason why shes getting health plan is to have assurance and not getting the risk of not being insured after paying all the premiums (honestly, refunding doesn't help).

Then, she met her friend who just became agent with company A. She already gave up trying to get health related plans and so she shared her story with her A agent. Because he is new, he really know nothing much about conditions which can or cannot be accepted. And also because he is new, he did not stop trying. He updates my friend everytime there's a progress. The first time he submitted, it was rejected. He didn't stop, he asked my friend to get hospital letter, doctor's name, employers' testimonials and a lot more details and try submitting again. After 2 months of processing the application with multiple request for additional information, he managed to get my friend covered for hospitalisation plan and personal accident plan with exclusion for psychiatric related condition. And so fortunate, my friend was hospitalised due to some physical injury 2 weeks after the plan was activated.

I guess above is a really good story to know that there are still agents who are willing to fight the case for you. However, I must say it is highly dependent on the condition of the mental state at point of application. My friend's suicide attempt was about 10 years ago.

Depends on the type of coverage being applied for. Very likely non standard terms will be offered by the insurer. Even if it is not disclosed, the reinsurer may know something about you and your other applications with other insurers.

Moral of the story, always disclose all medical information when applying for insurance.