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This CL is the preparation to split ArcSession running parts
from ArcBridgeService.
- Rename ArcBridgeService::State names to be consistent with
  terms used in other ARC modules.
- Remove unused CONNECTED from State.
- Migrate PrerequisitesChanged() and StopInstance() into
  RequestStart() and RequestStop().
- Rename some fields of ArcBridgeServiceImpl for consistency.
- Cleaned up include directives.

BUG=657687
BUG=b/31079732
TEST=Ran bots.

Review-Url: https://codereview.chromium.org/2577373002
Cr-Commit-Position: refs/heads/master@{#439875}