Machine Soldier can special summon Machina Fortress, as it is a Machina monster. Machina Fortress has an inbuilt special summon method, but this is a 'you can' and not a 'can only' thing, it can be special summoned by other effects if you wish.
Since Machina Soldier is a machine, you are also allowed to use it to pay towards Machina Fortress's own special summon cost.
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If the summoning conditions it can be Monster Reborned from the Grave Yard.
No, only the player who activated Flute of Summoning Dragon can special summon the dragons through its effect.
Not unless the special summoning effect specifically says you can, like The Shallow Grave does.
As long as you are Special Summoning before, or during the Battle Phase, then yes, that monster can attack.
While Toon Blue-Eyes is a special summon only monster, is it different in that it has no specific summoning method, ie, you 'can' use the one on the card, but that's not a 'can only' like, say, Chaos Sorcerer. So Toon monsters like Blue-Eyes Toon Dragon can be special summoned with cards like Monster Reborn and Flute of Summoning Dragon, but only if Toon World is active.