Yes. The plan is cross rail will use the HEX platforms at T2/3.

So I found it:
https://goo.gl/maps/nWbNNv1Qadq

You'd have to buy out Ocado West Drayton and the other businesses in that quadrangle between the present spur to the east, the lake to the south, the mainline to the north, and Stockley Road to the west. And I can see that the existing bridge over the mainline for Stockley Road might cause difficulties, particularly if you want something as complex as the points they've set up on the way west to London. But would it really be harder and more expensive to fit something in there than digging a 5.5 mile tunnel? :)

You've got to also consider the cost of remodelling the railway in that area which is already complicated - and has just been substantially upgraded with resignalling and overhead catenary (to facilitate GWR electric services to Maidenhead recently started)... :)

Overall the cost/benefit is probably on the side of a tunnel.

This is a big U-Turn for TfL who said the prices would be the same as the tube. :(

"Mayor Sadiq Khan said: “I’m delighted to announce that the cost of travelling on the Elizabeth Line in zones 1-6 will be the same price as a similar journey on the Tube – fulfilling a key manifesto pledge to deliver truly world-class transport infrastructure which is also accessible and affordable for all Londoners.”

They're still saying the prices will be the same as the tube...! :D

Surely this is going to result in a lowering of prices from HEx?! A 30 day advance fare Paddington - LHR is £12.20 plus my £2.40 to get down to Paddington, but Crossrail will be £2.50 cheaper as a walk-up fare and therefore only worth booking well in advance if you can get a £5.50, 90 day advance ticket. I never get the Connect as it is twice as long and I always book in advance so rarely cheaper, but I can only really see corporate types arriving at Paddington in a cab paying the £25ish walk on fare, everyone else would be getting a through-ticket from town? I would imagine that someone coming from town would be better of changing at LHR for T5 rather than Paddington although I suppose we will have to wait and see how the interchanges are at the various stations in terms of ease of navigating the system with luggage.

Other than LHR they are the same as tube prices. It also mirrors the current Heathrow Connect pricing structure. Crossrail never made a commitment that fares to LHR would match the tube fares but would compare to the Connect pricing structure - which is also outside of the tube pricing structure (and freedom / travel passes) didn't include trips to LHR.

I'll happily pay the supplement of £7 to save 1/2 an hour on a Farringdon - T5 trip rather than the district and Piccadilly lines.

Here is the Mayor's Decision Record that was actually published on the 2nd of March.

The zone 1-6 price cap will be the same but the single fare will be higher. This means if you're travelling around London before heading to the airport you'll not pay more than £12.50 all day, that's the same cap as the Tube and covers all TfL modes except the cable car and National Rail within the zones.

People still take Gatwick Express. I don't think Crossrail will have Advance fares.

If you are coming from or need to go somewhere on the Piccadilly or District lines taking the tube still makes sense.

That story says :)

I guess HAL still get money, but I'd prefer to use Crossrail than Heathrow Express where possible,

To be fair the HEX advance fares are more flexible than National Rail advance fares, on the HEX you just specify the day you're travelling rather than the specific train but the Crossrail fares beat most of the HEX advance fares (exceptions are weekend ones bought a long time in advance) it's also worth taking into account the price capping if you're using other tube, rail, bus services within London that day

Crossrail Fares Incl Heathrow Announced
 

Already being discussed here. (Although, to be fair, it's already halfway down the second page).