"Relinquished"’s effect to equip itself with a monster can only be activated during your Main Phase 1 or 2 since it is a Ignition Effect.
A monster equipped to
"Relinquished" occupies a Spell & Trap Zone of the controller of
"Relinquished". So if you already have 5 Spell & Trap Cards on the field you cannot activate the effect of
"Relinquished". Any Equip Spell Cards equipped to the selected monster are destroyed.
"Relinquished" gains the ATK and DEF of the monster equipped to it, but not the effects of an Effect Monster.
The selected monster is treated as a Monster Card when it is sent to the Graveyard, so the effects of
"Sangan" or
"Witch of the Black Forest" would activate, but the effect of
"Mystic Tomato" would not, since it was not destroyed as a result of battle.
You can not voluntarily destroy a monster equipped to
"Relinquished" but you can use
"Mystical Space Typhoon" or
"Emergency Provisions" to eliminate it.
"Relinquished" inflicts effect damage to your opponent whenever you take battle damage from a battle involving
"Relinquished", if it is equipped with a monster. This can occur when
"Relinquished" battles another Attack Position Monster, or when it attacks a Defense Position monster with DEF higher than its current ATK.