According to IWC, the movement in the new Da Vinci chronograph is developed and manufactured in-house.
Here is an excerpt from the IWC press release concerning the new chronograph movement which should answer your other queries.
"The case contains as its mechanical heart the manufactory chronograph calibre 89360, newly developed by IWC, which Kilian Eisenegger has created with his design team. And it is here that the Da Vinci project becomes truly exciting. The round automatic movement with a power reserve of 68 hours, a newly developed doublepawl winding system and the predominantly decentral chronograph mechanism with column wheel actuation, is an entirely new design based on the highest industrial design standard, Design for Six Sigma DFSS, which has been used consistently by IWC for some time. A so-called “robust design” was achieved in this way, in which every function and component in a closely networked process between design and subsequent production is inspected, tested, optimized repeatedly and checked thoroughly to exclude possible faults.
The automatic spring bridge already improved for the Cal. 80111 of the Ingenieur has been adopted from the ingenious winding mechanism design of Albert Pellaton. This is a central component, which carries the rotor and absorbs impacts from all directions. The pawl winding mechanism itself has nevertheless undergone a complete change. Two double winding pawls, making four in total instead of the previous two, transmit the energy of the rotor movement to the pawl wheel through push-and-pull movements. A dead angle is eliminated during winding, and the efficiency of the winding is increased by 30 per cent by the new positioning of the pawls, which now no longer lie one after the other, but are arranged in pairs opposite one another on the pawl wheel. They are not controlled by the cam disc (heart) as previously, but by a crankshaft similar to that found in an automobile engine. The index-free escapement system with a special, Nivarox balance spring produced exclusively for IWC exhibits clearly superior oscillation characteristics in return for a lower energy requirement and achieves a “quality factor” – as the relevant measurable variable is referred to – of more than 400, which lies significantly above that of most other high quality and highest-quality movements. Fine adjustment is effected via precision adjustment screws on the balance wheel ring.
For the first time, the chronograph movement with its flyback function, actuated via a classic column wheel, permits the indication of the aggregate time recording of hours and minutes in the familiar form of an analogue time display with two hands. It can also run continuously with the movement without any decrease in amplitude.
This feat of strength demonstrated by proprietary chronograph design also meets the high demands of a watch which does not bear the great name Da Vinci simply in order to embellish itself, but rather in order to live up to all that the name implies."
- SJX