Forgive me I do not have the numbers on all this but I'm sure someone will have the formula...
Do the hordes scale based off heatmap, player level or just the number of days in you are?
Hordes will be based off of player level (each player), game stage, number of deaths, etc..
Does noise matter during a horde night aside from affects on the heatmap following?
It will not effect the 7th day horde (or what ever day it is set to)
Do 7th day hordes scale dynamically during the encounter based on any factor?
Just the ones listed in first question
And lastly is it just an endless horde until 4AM or is there a finite number of specific enemies that spawn per 7th day?
Unfortunately no. Most hordes will end far before morning depending on player/group game stage.