I dont want to make this complicated, and didnt read through the full post BUT.
1) Were there enough bees to split? (dependent on how you did the split)
2) Is the split you made in the place of the original hive?
3) If not you need to put at least one food frame (maybe 2, dependent) Because the new bees/house bees wont just go out foraging)
4) Do you have enough bees/feed to facilitate them raising brood?
5) Do they have to much room for the box they are in?
If you removed a pile of nurse bees and installed a mated queen, and your slit is not where the original hive was, then you must make sure you give them pollen and nectar.
If same split is where original was the field bees will bring it in, assuming it is coming in.
Dont make the split complicated, Enough Pollen, nectar, the right age brood, and enough nurse bees to feed/ raise a queen, (If thats what your shooting for), with as little area to defend, for the amount of bees.
Or if you went another rout, QC, mated, enough nurse bees to take care of the brood plus Feed.
But if you leave the split in the place of original, think reverse.
If you make it when the foragers are home and move it somewhere (another yard they will re orientate. If you leave it in the same yard put something in front of the hive to MAKE them re-orientate.
Hope this wasnt to bad.