The parliamentary process to approve the Crossrail Bill looks to be coming to an end shortly, after the House of Lords committee hearing petitions against it, approving it while making only minor amendments. This was the last major hurdle for the bill, and the last chance for the public to object.
It now only has to pass a "committee on re-commitment" (whatever that is) and go for a final vote in the two houses - likely to be a formality - and then it's law. The bill provides powers and outline permissions to build the line, but not funding.
Looking at the committee's report, they were quite keen on a connection from Heathrow to the west (page 42), but decided not to require it be added to the scheme. They also liked the idea of extending the line from Abbey Wood to Ebbsfleet (page 36), but again, decided it could be built separately.
While we're on the topic, I've received an email from the Crossrail press office in response to this old post. They confirm the central section of the line will have Automatic Train Operation:
Crossrail is using Automatic Train Operation (ATO) in the central area from Ealing Broadway to Abbey Wood and up to Stratford station where it can be integrated with current automatic systems. ATO is a system in which all train movement control is automatic apart from the door operation and starting from stations.A quick Google reveals ATO has actually been an ambition for a while, but this confirms it's still on the table.
Safety information is continuously transmitted to the train in the form of electrical codes in the running rails which tell the train its permitted speed. For signal stops, a brake command signal in the running rail causes the brake to be applied and then automatically restarts the train when the signal is cleared.
The email also goes over the reasons for not specifying double deck trains (construction expense, dwell times, limited capacity gains, etc), and mentions the future extension from 10 to 12 car trains will allow a similar capacity gain (20% vs 30-40%) for much lower cost.