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Can you use heavy support/fast attack/dedicated transport options as they're outlined in Imperial Armour 1 in the Castellans of the Imperium detachment? For example, could I use the immobile basilisk batteries as a heavy support choice for the detachment, given that the battery is listed as a "heavy support choice for a Codex: Imperial Guard army", or is it only the units outlined in the book itself?

it depends on the wording in the imperial armour. In your example it would be no, because its not outlined in the castellans detachment. If the wording would be any imperium army can include, you would be able.

Via RAW the answer is "no" the Castellans of the Imperium detachment lays out very specificly what you are allowed to take.

the Troops section, for example does not say "You may take troops from codices SMs, AM, AS IA" it says "you may take tatical squads, scout squads, sisters squads, infantry platoons"

If they aren't listed, you can't take them. Simple as that. The only exception would be if IA 1 says that certain units can be used in detachments or formations. As IA 1 came before Formationhammer, that probably isn't the case.