Yes, Princess Celestia, Luna, and Cadence will get their magic back since the main 6 defeated Tirek and have been rainbowfied to help Equestria receive their magic back. If you want to watch it you can on YouTube or Dailymotion
Yes, she is Princess Celestia's adopted niece.
No. Only four princesses have been named in the show: Celestia, Luna, Cadance, and Twilight. Princess Papillon appears to have been an alternate version of Queen Crysalis created by the show's fans.
Princess Cadance will apear in Episode 10 "Three's a Crowd" on January 25. No mention has been made of Shining Armor.
No. Looking at the flashbacks to when Twilight was a filly, Cadance is noticeably younger. This suggests that she is relatively young, meaning that whe would have been born some time during Luna's 1000 year banishment as Nightmare Moon. The description of Cadance as Celestia's niece is not meant in the literal sense of the daughter of a sibling. If you believe the story in the book Twilight Sparkle and the Crystal Heart Spell, then Cadance is not even related to Celestia by blood, but was essentially adopted.
Yes, Cadance will appear in the My Little Pony Friendship is magic episode Twilight's kingdom.
That is highly unlikely. That would be too dark for My Little Pony. Remember that the show is targeted at young children.
I think you're thinking of Princess Cadance. She is pink, and has the crystal hear on her cutie mark. Check this link out to see if this is the one you are thinking of:http://images5.fanpop.com/image/photos/31900000/Princess-Cadance-my-little-pony-friendship-is-magic-31955391-646-646.png
Princess Cadance is Stella Jang and she is awesome! Moo.
She is the daughter of Princess Cadance and Shining Armor.
The identities of Cadance's parents are never revealed and no information is given about them in the show. However, if you take the book Twilight Sparkle and the Crystal Heart Spell to be canon, Cadance was found abandoned as a baby, her parents unknown.
She is officially Princess Mi Amore Cadenza, but in most cases she goes by Cadance.
Princess Cadance marries Twilight Sparkle's brother, Shining Armor.