Hi,
For vCenter in version 6.0 you can manage ESXi hosts with version: 5.5 and 6.0.
You can check this out on VMware Intercompatibility Matrix:
https://www.vmware.com/resources/compatibility/sim/interop_matrix.php#interop&2=&1=
So if you want to manage ESXi in version 6.7, first of all you have to upgrade your vCenter server.
Upgrade sequence:
https://kb.vmware.com/s/article/53710
About mixing ESXi versions in one cluster:
Generally it works. Usually, this is done to facilitate rolling upgrades. If you have a large 32-node cluster it's difficult to upgrade all 32 hosts at once.
But I am not sure if it is officially supported. If you need to mix HA/DRS cluster with different versions of ESXi remember that you must use VMware Tools, VM Hardware version etc. in versions supported by all hosts in cluster.