[RPG] Is the damage from the Magic Stone cantrip magical

As nothing special is indicated for hurling the bullet with a sling, the normal rules for sling range apply: 30/120.

Yes. You can sneak attack with any ranged weapon.

Throwing by hand, no. A pebble is not a finesse or ranged weapon.

Hurling with a sling, yes. See Sneak Attack in the PHB:

Sneak Attack (PHB p.96, emphasis mine)

Beginning at 1st level, you know how to strike subtly and exploit a foe’s distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon. You don’t need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn’t incapacitated, and you don’t have disadvantage on the attack roll. The amount of the extra damage increases as you gain levels in this class, as shown in the Sneak Attack column of the Rogue table.

Sneak Attack considers the weapon properties not the attack type. While not using the usual modifies, as per spell description, you are hurling a stone with a ranged weapon.

Since you normally can apply Sneak Attack to a sling shot, why should using an enhanced projectile be worse than that?

A rogue cannot access the Magic Stone cantrip inexpensively, so I'd consider this clever synergy.
Also the resulting damage isn't imbalanced.

The unofficial ruling by Jeremy Crawford is also a yes.

As DM, I'd allow it to work, given how Sneak Attack and magic stone are worded.