Yes, JioPhone does support Live TV. You just need to select the channel, which you want to watch and hit the button "play".
No. It is mandatory that you have to use Jio sim card in JioPhone.
Yes, JioPhone does have a 3.5 mm headphone jack.
JioPhone comes with 4GB Internal Memory. So, you can save as many as you want - depending upon the free memory on the phone.