It is important to have consistent time settings within the whole infrastructure. Some services strongly relies on the time synchronization and troubleshooting is much easier when the time is synchronized as well
(b) False
If the vCenter Server crash you would like to be able to restore the whole configuration from the backup. As a best-practice it is advised to perform the backups on the vCSA level through VAMI interface, not the infrastructure level backups using backup solutions like Veeam.
(b) False
vCenter Essentials can manage up to three hosts. vCenter Foundation can manage up to four hosts and vCenter Server Standard has no limitation in the number of managed hosts.
(a) Active Directory, Open LDAP, LocalOS, and Local Domain