The health insurance marketplace opened for business on Saturday and performed much better than last year, but some consumers reported long, frustrating delays in trying to buy insurance and gain access to their own accounts at HealthCare.gov. Thousands of people attended hundreds of enrollment events around the country at public libraries, churches, shopping malls, community colleges, clinics, hospitals and other sites. Insurance counselors and federal, state and local officials said they were trying to juggle two tasks — enrolling more of the uninsured and renewing coverage for those who already had it. Some of the problems became evident on Saturday just as Sylvia Mathews Burwell, the secretary of health and human services, was visiting a community health center in Manassas, Va.