"Tomorrow it is my last day."
ok you could say that, every spanish speaker person would perfectly understand you, becuase everything is ok..., but probably there are some rules about what should it be first (that i am not really aware, because spanish is my native language), but still if you say that it would "kinda" sound like a "Yoda" way of speaking, lol.
no, the exact meaning of ''último'' is ''the last one- , and when it's the last one, it is the final one... lol, but to know wich one you use it you have to know the context, just as in english for ''last and final''
Why is there no feminine version of ultimo? I figured since it was describing what kind of day it was that it would be ultima. I guess that's not the case...
no, it is not the case because "día" even if it ends with an "a" it is masculine. for example you could say "Mañana es mi última comida" (tomorrow is my last meal) now that comida is feminine you have to use último as feminin, it always depends on the subject you are talking about. normally every word ending with an "a" is femenine, but "día" is one of the few masculin words that ends with "a".
I think pasado as in "el dia pasado" means last as in previous, so in this situation it would not work as it would mean "tomorrow is my previous day"