Yep that should be fine, converter will just be doing a V2V so the hardware level of the source is not relevant.
Any recommendations on upgrading, like vers. 7 to vers. 10, or an issues with VMFS3 on old host and VMFS5.61 on new host?
I believe you can set the VM hardware version of the destination VM when you configure the job in VMware converter, so that takes care of the hardware version.
The difference in VMFS versions should be fine as well. The conversion process is not really reliant on the underlying components.