Persona 5

function:
in P3 the Persona was described as a "second face"- a true self within the psyche.
The evoker sends a electric shock to the brain wich stimulates the subconciousness-the "home" of the persona and therefore force the persona to awaken. This is only possible/nesicarry for weak personae (such as those of the Protagonists), strong personae, those of the Strega members, can be summoned at will and are able to maintain a physical form (as seen when Medea tried to kill Chidori).

who makes them, how did they discover it, etc

the chairman was one of the first to know about the persona,he might be the one who brought them. Yukas father was a scientist in the field of the persona, so that the evoker might be a way to bring out weaker persona
the whole shadow/Persona thing was greatly researched and discovered by the Kirijo group and the kids have to use Invokers since their personae are "weak"
following thought: evokers could be manufactures by the kirijo group
About Aigis (summons persona at will, too)
Aigis is a robot (or part of a series) that was produced to be a "life line" when the shadows do a large scale outbreak, her "evoker" was installed within her
The dogs invoker was the collar he wore, so his was a special model. means they have the possibilities to make new ones
problem here is. until the vid with yukas dad came up noone knew about the involvment of the Kirijo Group, exept for the chairman

assuming we have "strong" and "weak" personae we can also assume that there are "weak" and "strong" shadows.
Weak shadows are the regular ones, the glibberish mass crawling through the regular, random floors.
I believe that, since they have no real form until the fight starts, that they can only maintain their "battle form" during the time the party fights them.
"Strong" shadows (as well as the Arcana shadows) have a physical form resembeling the type of enemy on the map. Their Strenght might be so big, that they can stop the warping of the floors in a certain area (the boss floors) and even reach out of the Dark Hour (as seen against Hierophant and Lovers Shadows- Lovers lures them to the Love Hotel, Hierophant sets them asleep).

we remember the day junpei arrived? Akihiko said "now we can start exploring that thing"- means up until then no one has set a foot into tartarus (they went in a few floors, yes but no large scale exploration).
Until then they were hunting Shadows on the street (see October full moon, Kens Mom died during one of those operations) means they were already outside.
Since shadows have no appearent gender or mating behavior they seem to reproduce via asexual reproduction so one free roaming shadow can spawn a whole bunch outside.
Also during the Final, People change into Shadows because of NYX's influence (cutscene).

Why do they feed?

Shadows seem to be "Anti-Personae" (reference to P4), so while the Persona supports the Mind, the shadow feeds from it, sucking away all desires and drives from it- and therefore causing Aphaty. The way they "devour" is unknown to me, but since the Shadows in tartarus dont feed, they seem to have some kind of "Hive Stomach" sharing the resources the outside shadows get.

Why don't the Shadows destroy the town

2 reasons:
1st- The events during the Dark Hour do not affect the real world. But I have no proof for this theory
2nd- they dont have to. As seen in the Anime-cutscene where the shadows attack a Gekkoukan student he is stuck dumbfounded when he enters the Dark Hour.
The Shadows only seem to attack new persona-able persons, who cannot evoke or they choose their Prey and free it from its coffin.
Eather way, the shadows dont have to expect any resistance so no Magic is needed.

The Lobby is the entrance to tartarus, its pinned neatly to the ground. There is no need for it to rise.
The walls shifting at the side may be a symbol of the changability of the Tower

Only the Devices on boss Floors are two-way, so maybe this special Power is close to the Boss-follr phenomenon.

for the rest: simple teleporter, go in on one side, come out at the other