"And I already have a software that allows me to tweak the games coding" "but I need to know how to code in new mechanics New mechanics"
One kind of implies the other.
New mechanics is also not a fixed concept, and for that matter more tiles to a sprite is also not fixed. New mechanics can be as simple as you doing things it already does; jumping and firing a fireball would presumably only need you to trigger the fireball command it already knows from a jump which is basically already does, might even a single instruction change. Compare that to adding a radical new style of play (maybe you bring the super mushroom powerup from new super mario brothers), and possibly some level tweaks too so as to take advantage of it and that is a different matter entirely.
"Will I need to allocate more kb to the Rom"
Someone might know I guess but it is usually something you get to figure out for you and what you plan to do.
As a hint though, and assuming there is no nice commented disassembly for you to play with (which there is and that changes the best approach by making that the easier path), then when in different states (large, small, fire flower, maybe star, not sure what others exist here in this game offhand) then there is probably a call to display different sprites. Here I would probably make another state and where it normally fetches mario sprites (chances are not all are kept in RAM at all points) it will instead dutifully go off for your location you picked for luigi ones (and same probably palettes).