You can't use your factory glass for three reasons.

1) Carbon hatches are weak/flimsy and can't hold up to the weight of real glass.

2) Carbon hatches are weak/flimsy and don't have the rigidity to hold your glass without breaking it.

3) Carbon hatches don't give you a ton of weight reduction unless you also replace the glass with plastic.

Installation to the car is usually easy, and the lexan/acrylic window can be bonded in the same way as standard glass. Some hatches already come with the plastic in them. Make sure you don't buy a hatch with the "glass" screwed in place, that's shoddy and seriously weakens the hatch. Bonding the glass in place adds to the strength of the hatch and will not harm anything.

Carbon hatches, because of their lack of rigidity, often have problems sealing with the stock seals/weatherstripping. I would strongly recommend getting a new seal kit so the new hatch can seat to a virgin sealing surface.

I'm going to go on a rant here, but making a direct carbon (actually mostly fiberglass) copy of a stamped metal part is irresponsible. Carbon isn't the same as metal, and can't be treated in the same way when designing and making parts. I'm not talking hoods and trunks here, because they're unstressed sheet metal, and purely cosmetic, not semi-structural like hatches. The big problem is the weight of the glass and the very small rails that form the edge of the hatch (along the sides of the glass). It's hard to make that part of the hatch strong enough without making the hatch expensive and very labor intesive.
As you can tell, I'm not a big fan of carbon hatches, at least 95% of the ones on the market. The decent ones are neither affordable or readily available. It wouldn't be hard to make a good hatch, but I've never seen anything decent for under $1500-2000, and those are only available for limited vehicles.