Sekraken Tuskar Charge says specifically in the rule it only applies to a War Boar's Tusks and Choppa says it only applies to non magical weapons and doesn't apply to a model's mount. For Hatred (Dwarves) it applies to all the profiles for the chariot or mount that a Night Goblin character chose (And it would only be for cave squigs which already have Hatred (Dwarfs).
Impact and Stomp Attacks (for chariots) use the chariot's strength and there is only 1 chariot. A crew or horse cannot use the chariot's strength since they have their own strength, therefor they don't get Impact or Stomp Attacks. Same for cavalry, the impact or stomp attacks use the mount's strength, the rider can't use the mount's strength for their own.
For the Anvil of Doom, it is a war machine split profile, so the Anvil is the war machine and the crew is the one that can equip the magical runes since they need to be forged on the hand weapon, armour, or talisman of the crew. For the T10 rune, its inscribed on the model wearing the armour, so the crew would be T10. Since its a war machine, for shooting attacks it would be T7 (the toughness of the war machine) and for combat it would be T10 (the toughness of the crew)
For Challenges: Moving around for challenges has always been kinda vague. But it's not illegal for a champion to be in the corner for a challenge. If a unit gets flanked, and challenged, the champion can make way to the corner and accept the challenge. After combat, the champion would stay there until the unit turns, reforms, or when the unit completes its movement the command group gets repositioned into the new front rank (pg 198). So they would make way to the center of the unit after the challenge and combat is complete.
If there's a character there, the character can make way to get back into the fighting rank regardless. However, if they move through the ranks to occupy a space anywhere other than within the front rank of their unit, they must return to their previous position immediately once their unit is no longer engaged in combat.
So as an example, a unit with a character in the corner of the unit gets flanked. The charging unit challenges and the champion accepts. The champion would make way to the corner, switching with the character. The character would then make way to the file behind the champion to still be in base contact. After combat, since the character make way to a space other than the front rank, they would return to the corner and the champion would return to the center of the unit.