If metals shape the Investiture in Allomancy, causing a Steelpush or whatever, how is it that the mists can be used to perform the same feat? What is 'shaping' the inhaled mists into a Steelpush, if there's no metal "nozzle" to do so?
Consistently through the cosmere, once you have the power in hand and it has permeated you, will becomes your nozzle. This can be seen in Warbreaker, where the power has been distributed and inhabits the people. The nozzle idea is important for Magics that are drawing power externally, as it keeps the power from overwhelming and destroying you. (Which, basically, happened to Vin at the end of the Trilogy--she got consumed by the magic. She became something new, now, so it didn't KILL her. It destroyed what she was, transformed her into something else.)
So you see magics like on Sel and Scadrial where a specific nozzle is needed--as the power source is external, at least with Allomancy. Will and intent take a backseat, though still pop up on occasion. On Nalthis (and in a lesser way, Roshar) will and intent are more important, and what you are trying to do shapes the magic more directly.
A little direct manifestation in this is found in the subtle differences between Allomancy and Feruchemy. In Allomancy, when you enhance the senses, you just get a blast of power--and all senses are enhanced, whether you want them all or not. In Feruchemy, you can be more precise, and pick a specific sense to store. The power is internal here, and therefore more limited in how much you can draw--but you can also be more precise with its manipulation.
Note that Roshar Surgebinding is a special case, as the magical symbiosis there is stronger than it is on other worlds, as much of the magic involves bits of power who have become sapient.
How much crossover is there in use? Like if one "breathes" in the mists they can use it to power their allomancy. Could an Allomancer utilize stormlight to power his allomancy as well?
Most of the magics can be hacked together in one way or another, but some are easier to interchange than others.