One pool with multiple VIPs using it-how many health checks will occur to the members?

Health check is defined on a per-pool or per-pool member basis. Number of VIPs/Virtual-Servers using a single pool shouldn't cause the number of health-checks to increase in number. Assuming all the pool members serve similar function (usually the case), it is recommended to have a single health check at the pool level and make sure the pool member's inherit this health check.