The 312's were an option starting in '56. Yes, Ford used the 'Thunderbird' name on 292's and 312's in their other cars for marketing/sales purposes, often with optional 4bbl carb and dual exhaust.
The '55/'57 T-Bird has a longer/lower/narrower engine compartment than the sedans and some of the different parts are; exhaust manifold, oil pan, water pump spacer, timing cover/motor mounts... so the engine would fit into the car. But the basic 292/312 block is the same as other Ford (& Mercury) vehicles.
Various performance engine options were usually offered in T-Birds or other top-of-the-line models first, but by '57 could be special ordered or dealer installed in effectively any Y-block powered car.
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