No, it can only be special summoned initially from your hand by removing one earth monster from play.
Effects that special summon monsters from deck, cannot special summon a monster which is 'special summon only' because these monsters have to follow their own summon method. So you cannot special summon Relinquished using Mystic Tomato, it has to be Ritual Summoned or otherwise summoned by a card that says it can summon Ritual Monsters.
Likewise, Gigantes can't be special summoned from deck by an external effect, and of course can't use its own effect while it is still in the deck.
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No, "Uria" can only be Special Summoned from your hand.
Relinquished can only ever initially reach the field by being summoned from hand, using an appropriate Ritual Spell Card - or by any card that specifically lets you summon a Ritual Monster from other zones.Relinquished cannot be special summoned from deck by cards like Reasoning, or Mystic Tomato, etc.
It can't be Normal Summoned or Set, and can't be special summoned except by removing from play a Stardust Dragon from your Extra Deck.
You can tribute a special summoned monster, yes.
um, yeah... all monster can be normal summoned, flip summoned, special summoned etc unless specified otherwise. eg, ancient gear golem says "this card cannot be special summoned".