While you wait for Martha's response, here is an example of the eligibility rules for the state of Texas. In this case (and probably all others), the answer to both your questions is yes.
Eligibility
An individual is eligible (for Health Pool coverage) IF under age 65 and has been for at least 30 days and remains a legal resident of Texas and a United States citizen, or a permanent resident of the United States for at least 3 continuous years, and IF the individual provides the Health Pool's administrator evidence of one of the following:
1. Notice of rejection or refusal by an insurance company to issue substantially similar individual health insurance due to health reasons;
2. A certification from an agent or salaried representative of an Insurance Company, on the Pool's Application form, that states the agent or representative is unable to obtain substantially similar individual Health insurance for You with any state-licensed Insurance Company, which the agent or representative represents, because You will be declined for coverage, as a result of Your medical condition, under the underwriting guidelines of the Insurance Company.
3. Either an offer (by an insurer or HMO) to issue or an in-force substantially similar individual health insurance policy that excludes a medical condition or conditions;
4. Either an offer (by an insurer or HMO) to issue or an in-force substantially similar individual health insurance policy at a premium rate greater than the current Health Pool rate;
5. The individual has been diagnosed with one of the Qualifying Medical/Health Conditions.
An individual is also eligible (for Health Pool coverage) IF under age 65, remains a legal resident of Texas, and IF the individual has maintained health insurance coverage for the 18 months preceding application for coverage to the Health Pool, with no gap in coverage of greater than 63 days, provided the last health insurance was through an employer sponsored plan, church plan, government plan, or another state's high risk pool. (United States citizenship or permanent residency is not required for this eligibility category only.)
Dependents are also eligible for Health Pool coverage. If the eligible individual is a child, family members of the child who have been for at least 30 days and remain legal residents of Texas and United States citizens and who reside with the child are also eligible for Health Pool coverage.
REW