DevTools: Port some network tests.

Bug: 667560
Cq-Include-Trybots: master.tryserver.chromium.linux:linux_mojo
Change-Id: I196707ea89f0c2b1b372a57b53f866fe4f03d76f
Reviewed-on: https://chromium-review.googlesource.com/783820
Commit-Queue: Eugene Ostroukhov <eostroukhov@chromium.org>
Reviewed-by: Will Chen <chenwilliam@chromium.org>
Cr-Commit-Position: refs/heads/master@{#518827}