Make FakeSettingsProvider thread-safe.

Synchronize all accesses to mDb to ensure thread safety, because
ArrayMap is not thread-safe. It's also more realistic, because
SettingsProvider does lock internally when accessing settings.

Also, make internal utility methods static, and remove
recently-added debug logs.

Flag: EXEMPT TEST_ONLY
Test: test-only change
Change-Id: If850129bb627dcd475ac6cac35b9d9b6be063280