For a globally routed overlay mesh, have a look at https://yggdrasil-network.github.io/
The latest version actually uses the Wireguard TUN library https://yggdrasil-network.github.io/2020/02/21/release-v0-3-...
Kubernetes does not use anything for the service mesh internally - as it does not provide a service mesh.
By this I can only assume you mean some popular CNI provider uses wireguard, but out of the ones I know of (flannel, weave, calico, canal, romana) I don't believe any use wireguard.
No it doesn't. There are some CNI plugins that use Wireguard, but it's not standard in any way (like any other network plugin, really).