[Google employee] Yes, you can use TPUs in Compute Engine and GKE, among other places, for whatever you'd like. I just checked and the v6 are available.
Google employee here. Not the case. Cloud Run doesn't run on Kubernetes. It supports the Knative interface which is an OSS project for Kubernetes-based serverless. But Cloud Run is a fully managed service that sits directly atop Borg (https://cloud.google.com/run/docs/securing/security).