Typically, and unsurprisingly, proprietary information (to include part numbers, schematics, etc.) is closely guarded by companies. As such, I am not sure how much information you can expect to receive without significant effort on your part. For starters, you can be sure that Apple will not release its specifications or parts list.
Take a look at the iFixIt tear down of the iPhone 6s and you will see no mention of the compass chip. Doing some more research, you can find the ChipWorks parts list of the iPhone 6s, and again, the compass part number and manufacturer are listed as "unknown." The reason for this is the A9 system on a chip, which now incorporates a number of sensors -- including the magnetometer -- which were discretely included in previous models. Furthermore, you can read about the M9 co-processor that sits inside the A9 and is used to process sensor data.
Despite the lack of information, I would wager that the AK8963C is the digital compass used in the iPhone 6s. I base this speculation on the fact that the AK8963C was used in both the iPhones 5, 5s, and 6. In fact, the same IMUs are used between most, if not all, of these models, which suggests that Apple has invested in this set of sensors and is content with their performance. Lastly, I am not intimately familiar with the iPhone 6 and 6s, but again, I would wager that the difference between the two, at least in terms of capability, is marginal. Assuming that the AK8963C is the compass, the datasheet is available, and should answer several high-level and many low-level questions that you have.
As for calibration--yes, the AK8963C needs it. Again, I suspect that you will have a difficult time getting any manufacturer to detail the procedure, especially Apple. Among other relevant things, the datasheet highlights some tuning parameters, but at the end of the day, this is all happening in software--whether you require the user to calibrate, or handle it automatically, calibration is almost certainly happening. Still, this article and the many like it suggest that perhaps the iPhone 6s sensor outputs are not a accurate as your observations exist.