Yes vcenter 6.0 U3 is requirement ,
Can ESXI 6.0 U1 and U3 exist in the same cluster, is there any functional limitation? Such as HA, VMotion
Yes you can put in same cluster, but not for long time, recommendation all hosts should be on same build
It is always suggested to keep the vCenter version equal or higher to the ESXi hosts.
Since you have stated that few of the hosts are running on U1 and few on U3, it is advised to keep the vCenter at version 6.0 U3 or the latest.
You can have mixed build number of 6.0 ESXi hosts within the same cluster however vMotion may not work if the hosts are on different hardware and no EVC enabled.