Gaining control of a creature doesn't cause you to gain control of any Auras or Equipment attached to it.

The creature you gain control of must attack during your turn if able.

Besmirch can target any creature, including one you already control or one that's untapped.

Being goaded isn't an ability the creature has. Once it's been goaded, it must attack as detailed above even if it loses all abilities.

If the creature doesn't meet any of the above exceptions and can attack, it must attack a player other than the controller of the spell or ability that goaded it if able. If the creature can't attack any of those players but could otherwise attack, it must attack a planeswalker an opponent controls, a battle an opponent controls, or a player who goaded it.

Attacking with a goaded creature doesn't cause it to stop being goaded. If there is an additional combat phase that turn, or if another player gains control of it before it stops being goaded, it must attack again if able.

If a creature you control has been goaded by multiple opponents, it must attack one of your opponents that hasn't goaded it, as that fulfills the maximum number of goad requirements. If a creature you control has been goaded by each of your opponents, the creature must attack an opponent (rather than a planeswalker or battle), but you choose which opponent it attacks.

If, during a player's declare attackers step, a creature that player controls that's been goaded is tapped, is affected by a spell or ability that says it can't attack, or hasn't been under that player's control continuously since the turn began (and doesn't have haste), then it doesn't attack. If there's a cost associated with having a creature attack a player, its controller isn't forced to pay that cost, so it doesn't have to attack that player.