Can Google Kubernetes run Apache Mesos frameworks on top of it?
Yes and no - you can run applications in containers on kubernetes, and you can run kubernetes on mesos.
In fact, Cassandra is one of the standard kubernetes examples. And there is an example of kubernetes on mesos.
Yes!
The new "DaemonSet" abstraction in Kubernetes provides great support for running data processing and storage systems like HDFS and others relying on daemon-based architectures...
"Users might want to implement a sharded datastore in their (Kubernetes) cluster. A few nodes in the cluster, labeled ‘app=datastore’, might be responsible for storing data shards, and pods running on these nodes might serve data. This architecture requires a way to bind pods to specific nodes, so it cannot be achieved using a Replication Controller. A DaemonSet is a convenient way to implement such a datastore."
See: https://github.com/kubernetes/kubernetes/blob/release-1.1/docs/design/daemon.md