Do my pre-existing conditions disqualify me for medical insurance?

If I have a pre-existing condition, does that mean I will not be apply to qualify for the medical insurance provided by my teach abroad employer?

Each school has a different medical insurance policy and provider, and whether your pre-existing conditions would disqualify you depends on the policies of the provider. It's also good to note that almost all countries require a medical screen in order to qualify for a visa. Policies differ from country to country, but not being able to pass a medical screen can disqualify someone from visa eligibility.