Does anyone know, if the cross farm publishing of UPS service is possible when consumer is SharePoint 2013 and publisher is SharePoint 2016, both on premise.
Yes, this scenario is possible. More details can be found in Share service applications across farms in SharePoint Server 2016
Additionally, a SharePoint 2013 farm can consume services from a SharePoint Server 2016 farm but a SharePoint Server 2016 farm cannot consume services from a SharePoint 2013 farm. For example, a SharePoint 2013 content farm can access a SharePoint Server 2016 farm, but a SharePoint Server 2016 content farm cannot access a SharePoint 2013 farm.
There are some limitations special to UPS, so it is useful to fully understand the linked article before deployment.
Yes that is supported scenario, You can publish the UPA in SharePoint and 2013 can be consumer.
if you have MySite in both farm then some of the features will not work in SharePoint 2013 farm. as the official statement.
The User Profile service must reside in the same datacenter as the content it supports — The performance of social features require the User Profile service application to be located in the same datacenter as My Sites, team sites, and community sites.
If you have mySite in both then couple of Profile related active may affected. Also make sure all the farm in same domain.