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.
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".
No. Unless specified otherwise, a monster's Special Summon text applies for when it is in your hand only. You cannot use Gigantes' own effect to Special Summon it from any other Zone.
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.
No, you can't. The only time Hamon can be special summoned is while he's in your hand, by following the text on his card. If a monster can be special summoned from other zones, it will say so on the card.
Yes, but with skill drain.
No, they cannot be special summoned except by following the text on their cards, and this can only be done while they are in your hand.
Any appropriate effect can summon an Earthbound Immortal from deck, they have no innate restriction against this. Cards like 'Reasoning' can do it, and in the case of 'Wiraqocha Rasca', that one can be summoned by 'Mystic Tomato' (though it does not get its ATK gaining effect unless Normal Summoned).
As long as the 'Cyber Twin Dragon' was properly summoned initially, by Fusion Summon, and was then destroyed, then yes, you can resummon it from the graveyard with 'Call of the Haunted'. If the 'Cyber Twin Dragon' got to the graveyard by the following methods - sent from Extra Deck by 'Gale Dogra', special summoned but not Fusion Summoned by 'Cyber Stein', or had its Fusion Summon negated, then it cannot be special summoned from the graveyard.
You can tribute a special summoned monster, yes.
The Deck is shuffled whenever something is 'returned to' it, or removed due to a search effect. Yes, it must be shuffled after another Gladiator Beast is Special Summoned on resolution.
Unless a monster specifically states otherwise, its special summoning text can only be used while it is in your hand.