I started a pod in kubernetes cluster which can call kubernetes api via go-sdk (like in this example: https://github.com/kubernetes/client-go/tree/master/examples/in-cluster-client-configuration). I want to listen some external events in this pod (e.g. GitHub web-hooks), fetch yaml configuration files from repository and apply them to this cluster.
Is it possible to call kubectl apply -f <config-file> via kubernetes API (or better via golang SDK)?
As yaml directly: no, not that I'm aware of. But if you increase the kubectl verbosity (--v=100 or such), you'll see that the first thing kubectl does to your yaml file is convert it to json, and then POST that content to the API. So the spirit of the answer to your question is "yes."
This box/kube-applier project may interest you. While it does not appear to be webhook aware, I am sure they would welcome a PR teaching it to do that. Using their existing project also means you benefit from all the bugs they have already squashed, as well as their nifty prometheus metrics integration.