unlike the other threads ive read about this land Izzet Boilerworks, this question has to do with the rules behind the usage of the double mana ability. I believe that when this land is tapped to produce mana, you are only able to use the island and mountain mana together specifically. for example, using it in part to cast a commander or another creature/spell that requires more than one specific mana cost such as Zedruu the Greathearted. whereas a friend of mine believes that these 2 mana can be used separately to cast separate spells. Also, they believe they can use any one of these mana as a source of colourless to cast any spells. for example, if they are using a red deck, then they can tap izzet boilerworks for one red specific, and one blue to use as colourless to cast a card such as Volcanic Hammer. Any answers would be great thanks.
Mana is not tied together the way you think. It just goes into your "Mana Pool" and then is used from there. If you generate UR from Izzet Boilerworks you can then cast a Lightning Bolt and a Brainstorm. Or, you can cast a Stormchaser Mage. Or, to use your example, you can cast a Volcanic Hammer using the Red mana for the red requirement and the Blue mana for the Generic (not colorless) requirement.
To be clear, if the mana requirement is a number in a circle, it is "Generic" meaning any color can be used to cast it or you can use Colorless mana. However, if it is a then you must use colorless mana.
Mana is not tied together the way you think. It just goes into your "Mana Pool" and then is used from there. If you generate UR from Izzet Boilerworks you can then cast a Lightning Bolt and a Brainstorm. Or, you can cast a Stormchaser Mage. Or, to use your example, you can cast a Volcanic Hammer using the Red mana for the red requirement and the Blue mana for the Generic (not colorless) requirement.
To be clear, if the mana requirement is a number in a circle, it is "Generic" meaning any color can be used to cast it or you can use Colorless mana. However, if it is a then you must use colorless mana.