A creature has been dealt excess damage if one or more sources dealt more damage to it than the minimum amount of damage required to be lethal damage. In most cases, this means damage greater than its toughness, but consider the damage already dealt to it that turn.

Even 1 damage dealt to a creature from a source with deathtouch is considered lethal damage, so any amount greater than that will cause excess damage to be dealt, even if the total amount of damage isn’t greater than the creature’s toughness. Note that a source of damage having deathtouch has no effect on damage dealt to planeswalkers.

A planeswalker is dealt excess damage if it’s dealt damage greater than its current loyalty.

If a permanent has more than one ward ability, the abilities trigger individually. The spell or ability will be countered if either of the ward costs aren’t paid.

Rith’s ability will trigger as long as an opponent controlled the creature as excess damage was dealt to it, even if the creature is no longer on the battlefield or you control it at the end of the turn.

It doesn’t matter whether a creature, spell, or ability you control deals the excess damage, only that excess damage was dealt at some point during the turn. For example, if a 4/4 creature an opponent controls is dealt 2 damage by a spell you control and later that turn is dealt 3 damage by a spell another player controls, Rith’s ability will trigger.