Hi elchoriz0

First of all check the upgrade path from 6.1 to 7.10.1. Per below doc, direct upgrade from 6.1 to 7.10 is not compatible. Instead you can first go to 7.8 and then to 7.10:

VMware Product Interoperability Matrices

Second check if 7.10 is compatible with your current vcenter and esxi hosts versions.Check the link below, it is compatible with vcenter 6.0.0 and above:

VMware Product Interoperability Matrices

Next if you have any thinclient or zeroclient in your environment, make sure they are compatible with horizon 7.10.1 prior to upgrade:

https://www.vmware.com/resources/compatibility/pdf/vi_view_guide.pdf

Then perform the upgrade as per below guide:

https://docs.vmware.com/en/VMware-Horizon-7/7.8/horizon-upgrades.pdf

https://docs.vmware.com/en/VMware-Horizon-7/7.10/horizon-upgrades.pdf

Regarding agent compatibility, it is backward and forward compatible upto 1 version. So if you are running 7.10 connection server, you can install 7.9 or 7.11 agent. However it is always recommended to use same connection server and view agent versions unless told by vmware support.