Automatic merge from submit-queue (batch tested with PRs 62445, 62768, 60633). If you want to cherry-pick this change to another branch, please follow the instructions <a href="https://github.com/kubernetes/community/blob/master/contributors/devel/cherry-picks.md">here</a>.

Local up cluster enhancements

**What this PR does / why we need it**:

Networking in a cluster brought up by hack/local-up-cluster.sh was broken because kube-proxy fails to start: connectivity to the Internet is okay, but anything involving communication among services (for example, starting cluster DNS) fails.

Debugging this took a while because there was no indication in the output of hack/local-up-cluster.sh that something had gone wrong. There were also some harmless "no such process" errors during cleanup.

The kube-proxy startup issue was fixed in parallel by PR #60431 but that fix turned out to be incomplete, so this PR uses a different approach, suppresses the harmless error messages (caused by a race) and also makes it more obvious when processes die by checking them regularly.

**Special notes for your reviewer**:

I used

     KUBE_ENABLE_CLUSTER_DNS=true NET_PLUGIN=kubenet hack/local-up-cluster.sh -O

to start the cluster. Check the kube-dns pod and its logs to see how kube-dns fails to communicate with the API server.

I've left out health checking of kubelet when run under Docker because that isn't something that I have used myself yet and I wanted to send the enhancements without further delays. I can try to add that later once you agree that such a health check is useful.

**Release note**:
```release-note
fix network setup in hack/local-up-cluster.sh (https://github.com/kubernetes/kubernetes/pull/60431)
better error diagnostics in hack/local-up-cluster.sh output
```