1. Remove only 1 of the ESXi servers from the cluster. Can this be done?
Yes, my recommendation is place this host in Maintenance Mode and move to outside of cluster... take a look at documendation: Remove a Host from a Cluster
2. Can I prevent 1 particular ESXi host in the cluster from performing any HA related processes, such as migrating VM's to or from itself?
Not 100% if I understand you, but yes, you can configure Admission Control and select the policy "Specify a Failover Host", take a look:
Specify a failover host
With the Specify a Failover Host admission control policy, when a host fails, HA will attempt to restart all virtual machines on the designated failover host. The designated failover host is essentially a “hot standby”. In other words DRS will not migrate VMs to this host when resources are scarce or the cluster is imbalanced. Please note that when selecting this admission control policy it is by no means a guarantee that when a failure occurs all VMs that will need to be restarted actually are restarted on this host! If for whatever reason a restart fails or not enough resource are available the VM will be restarted on a different host!
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Richardson Porto
Senior Infrastructure Specialist
LinkedIn: http://linkedin.com/in/richardsonporto