Obviously. Fulfillment of the Contract's effect is that you pay 800 lp and special summon a ritual monster from your graveyard, and when the equip card is destroyed, the ritual monsters destroyed.
As usual with monsters who can't be Normal Summoned, the Ritual Monster must have properly been summoned first before you use Fulfillment of the Contract. You cannot simply discard a Ritual Monster and summon it with that card.
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No, because it wasn't 'properly' special summoned. To be able to special summon a Ritual Monster from the graveyard, it has to be initially summoned by Ritual Summon. Ritual Foregone does not Ritual Summon.
Only if the card specifically says it can summon a Ritual Monster, like Ritual Foregone. Otherwise, you can't do it, cards like A Hero Emerges, or Monster Gate, cannot special summon a Ritual Monster.Also if you summon the Ritual Monster properly, by Ritual Summon, and it is then sent to the graveyard for whatever reason, then you may bring it back to the field using cards like Monster Reborn. However you cannot simply discard a Ritual Monster from hand and try using Monster Reborn straight away, they are a form of special summon only monster, simply by being Ritual Monsters.
only if the monster has been summoned to the field, and the summon was not negated. also, if the card says 'this can only be -insert summon type- summoned by -insert ritual/Special summon info- ritual summon only (this card can only be ritual summoned by) -Only ritual summon Special summon only(This card can only be Special summoned by) -Only special summon, hope this helps.
Relinquished is Ritual Summoned with the Ritual Spell Card Black Illusion Ritual. It requires a monster as a Tribute to Special Summon Relinquished from your Hand. Once Relinquished is successfully Ritual Summoned, if it is sent to the Graveyard, it is eligible to be Special Summoned from it. You cannot Special Summon Relinquished from the Graveyard unless it was successfully Ritual Summoned first.
Just use a ritual spell and read its effect. You also need the ritual monster that it says on the card.