Are the characters loaded from a custom spreadsheet?
+ what smartphone apps have you used that you liked?
Yes, you can save/load your characters in a textfile in the "Actors" subfolder. If you open it with a texteditor you see that they are stored quite simple.
I accumulated a small rogue gallery that I can pull out at any time. (Rummage through the barrens? surprise gangfight!)
Also, for adventure modules, I can prepare potential combatants and put them all in one file.
I don't like fiddling with my phone at the table, but a friend manages his fights with
Next Pass and is quite happy with it.
https://eigertech.wordpress.com/next-pass/Would like "primary fields" (i.e. value input fields that are the original input, not a field that pulls the data from another field) to be shaded/bordered/or otherwise indicated.
Would like fields that pull from other fields to change color/give an alert if their value has been changed from that of the primary field.
Well, the whole attribute tab is a primary field, e.g. limits pull from nearly all attributes. But I see what I can do.
The fields that are calculated only do so if they are empty. Otherwise they assume that you know what you do

(Because of the myriad of ways (ware, magic, qualities, etc) that values may differ from basic calculation.
Fight page
A way to add/subtract initiative dice and rating to the actors (like someone casting Increase Reflexes in the middle of a fight, etc.) and keep track of that (an input field for the added dice and rating and a toggle box?)
On the fight page you can double click on the actor in the list to open it on the actor page. There you could edit his ini values in depth and make a notice with the "effect" button.
(This does not affect the archetype or other instances of the actor, e.g. if one ganger hits jazz, the other carbon copies of him are not affected)