Japanese widget:

http://web.archive.org/web/20120716121633/http://hpcgi1.nifty.com/mickeyinu/fe/rand/fe_torakia.html

Loose translation guide for the above widget (Thanks to twitch user mor_mot!):

Basically, you control which of the 64 seeds you want to look at with the drop down menu in 5th section, above the mess of Level Up info. Sections 2 and 3 can be used to look at the list itself.

The bottom section is some kind of fight calculator but I don't know if it accounts for the battle prediction you have to sit through or not. I prefer to look at the lists and do my own battle calculations to verify the route, especially since it seems to only look at one seed at a time.

Which of the 64 seeds you are in isn't manipulable by human players, but advancing the RNG is discrete like in some other titles:

-Pressing X on a unit to open their status screen clears the RNG and resets the position to 0

-Moving a unit diagonally 1 square burns 1 RN

-Moving a unit with a movement star burns 1 RN

-Opening the battle prediction screen burns enough RNs to simulate the fight. If you want to fight, you'll burn through a new set of RNs for the actual battle. You can press left or right on the D Pad if there are no other enemies in range to reload the same battle prediction screen and burn RNs at a rapid pace.

-In the battle screen window, just as in combat, numbers are only burned until one of the combatants would die or the combat otherwise ends.

-When you attack: --First, whether you'll attack twice is calculated, before RNs are burned

--Then, if you have Adept or Astra, you'll check for each attack you are scheduled to do (even if you kill your opponent before you get to all your attacks), rolling an RN to see if the skill triggers. ---If you have 0 Attack Speed, you won't roll for Adept.

--For each attack, you'll roll for Critical Hit, then a junk number (presumably battle animation), then for your hit rate.

--If you have Luna, you roll for Luna before each attack, and if it triggers you don't roll for hit on that attack.

--If the enemy has the Big Shield skill, Big Shield will roll before each attack, after Luna is rolled. Big Shield will not take effect if Luna is successful, but the number will still be rolled either way. If Big Shield activates, you don't roll for hit on that attack.

-The order that the RNG checks for stat growths when leveling up is HP, Strength, Magic, Skill, Speed, Defense, Build, Luck, Movement. The RNG rolls for every growth even if it's 0 (like Saphy's movement growth)

-You won't roll for staff hit if the staff user has 10 skill

-When a unit moves to a square and has multiple equivalent distance options to travel there, the game makes its choice by starting at the destination, then choosing which square to approach it from recursively until only one fastest path is possible. It makes this approach choice using this function: https://docs.google.com/spreadsheets/d/1qyuOrEsquPkoPkZZkdNPVXEPVoJ9-y3690up88R0fX8/edit?usp=sharing

--For example, if a unit moves 2 squares S and 1 square E with no terrain, the RNG is first called once. If the above function outputs 0, then the character will move 2S, 1E and no further numbers will be pulled. If the function outputs 1, the "destination" will move to the square 1S, 1E of the unit, and the RNG will be called again to determine whether the until will move 1S, 1E, 1S (0), or 1E, 2S (1).

Notably, all 64 seeds have a 94 at position 35 (which is useful for Hammerne staff misses) and a 12 at position 47 (which can help increase the probability of critical hits or trigger a movement star on 3+ star allies)

If you have more information about how specific skills work or how enemy AI burns RNs in each chapter, please let me know and I'll revise this guide accordingly.