Yes, Oppo K1 does have the Gyroscope sensor.
Yes, Oppo K1 does have a 3.5 mm headphone jack and it also comes with an earphone in the box.
Yes, Oppo K1 has the in-display fingerprint scanner.
Yes, you can record 4K videos on Oppo K1.
No. Oppo K1 does not have the FM radio support.
Keeping in mind that the Oppo K1 is the only phone with an in-display fingerprint sensor in its price band, the launch price of Rs. 16,990 is not too bad.
At the price, it has great performance, a good battery, impressive cameras and much more. It is also the cheapest smartphone you can get with an in-display fingerprint sensor.