Yes, you can use Airtel sim card in the JioPhone but the Airtel sim card will work only on 2G network.
JioPhone comes with 4GB Internal Memory. So, you can save as many as you want - depending upon the free memory on the phone.
Yes, JioPhone does have a 3.5 mm headphone jack.
Yes, Jio Music App will be inbuilt available in JioPhone.