best champ for never losing a tower?

Lots of mages have good waveclear and range; Lux, Ziggs, Xerath, Morgana, Malzahar, and Anivia come to mind as a few examples. Xerath is probably best among them, though, since his passive allows him a lot of mana sustain.

Best champ for never losing a turret? You're kidding right? There are so many factors involved in defending a turret like how many enemies are pushing, minion waves, number of teammates you have, how much health the turret has left, etc. There are situations where you won't be able to defend your turret in which case, letting go of the turret is much better (so you can heal up, group, and defend the next turret). In general, if you wave clear the enemy minion wave, its harder for the enemy team to tower siege so a champion that has sustained AoE dmg, like anivia, ziggs, and malzahar will be able to wave clear effectively. But its impossible to never lose your tower without your team's help.

you will be able to defend when you are alive and when shortly after you die

Heimerdinger with teleport

Having played both Ziggs and Xerath significantly, I would say Xerath takes the cake here. He can hold his own even against a Malzahar or Heimer so long as he is efficient with mana.

Probably Ziggs or Xerath