No, they are not 'on the field', ie, they cannot be targeted or affected by effects that work on a card on the field. As a further example, a Sangan used as a material monster, will not trigger if it is sent to the graveyard either by the Xyz monster's destruction, or effect.
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For Polymerization, the Fusion Components/ Fusion Material Monsters can either be in your hand or on the field, or a combination of both.
No, you cannot use Fusion Substitute Monsters for "Future Fusion". You can, however, use Fusion Substitute Monsters for "Chain Material" as long as those Fusion Substitute Monsters exist on your field or hand. The reason Fusion Substitute Monsters cannot be used from your deck is because they have no substitute ability while in the deck and thus cannot be used as replacements for other Fusion Material Monsters.
Gemini Monsters are normal or special summoned as normal, but when they arrive on the field, they are considered Normal Monsters and have no effects. The next time you are allowed to Normal Summon, you can 'second summon' them, ie, they count as being summoned again, even though they never leave the field. This turns them into effect monsters and switches on their effect. Note that if you are trying to 'second summon' a Lv5 or higher monster, no tribute is needed.
Face-down monsters are indeed monsters for the purposes of cards which count monsters on the field or affect all monsters.However, if a card effect specifies a monster with a specific type, attribute, ATK, etc., it will ignore face-down monsters because those values are unknown in game terms.Note: monsters used as Equip cards are not considered monsters.
Generally, Synchro Summoning sends cards from the field to the Graveyard. There are some cards that allow you to use monsters in your hand as Synchro Material Monsters instead, such as Eccentric Boy.Eccentric BoyAttribute: WINDType: Spellcaster/Tuner/EffectLevel: 3ATK: 800DEF: 200When using this card as a Synchro Material Monster, the other Synchro Material Monsters is 1 monster in your hand. The Synchro Monster that used this card as a Synchro Material Monster cannot activate its effect, its effect(s) is negated, and is removed from play when removed from the field.