Propagation of voltage induced in coil

Guess I need your help again. After simple DC circuits I feel I can't grasp concepts of EM induction particularly and AC in general properly. Especially in case of induced EMF, motional EMF is more or less ok. Actually there is a lot of questions, and I tired of finding answers so I try to generalize this all in example below.

Let's say we have a some stationary coil (it can be coil inside AC generator or transformer's secondary winding coil etc) with really long output wires (all the way across city like in Feynman's lecture) and some load at the ends of the wires (voltmeter / light bulb or even there will be open ends, looks like it doesnt matter at all). There is total equilibrium, no current, no any fields anywhere, nothing.

Now we suddenly change magnetic flux in the coil area, e.g. pushing magnet in it, here things become confusing.

2 different points of view:

Some say in the case of EM induction there is no potential difference at all anywhere, EMF itself drive current all around circuit (if it closed of course).

In this case I can't understand how current can be driven far away from coil, because I thought there must be usual electric field inside wires provided by surface charges but here we obviously don't have any charge on wires since there is no PD at all. Same I cant't imagine how current in wires can be supported by means of curly e-field since its force lines form loop. Well, maybe there is some other mechanism.

On the other hand others say that there will be potential difference between the ends of coil's wires (as confirmation AC generator definitely make some charge separation exactly this way and have PD between it terminals).

If this point of view is correct then I can't understand how exactly this PD established.

Because as I know PD can't just appears between ends of 2 wires, first there must be point / place where PD exactly generated, second if wires attached to that point then all wire must gain the source potential and not only it end (or if PD is constantly changing then wire's would continue to recharge as well).

And finally this process not instantaneous since this PD / conservative e-field / wave will need some time of propagation (couple of nano- or picoseconds, don't know) before it reaches the ends and so voltmeter can detect it.

So my main problem is that I can't understand where actual point of generation of potential difference in this case if it exist here at all.

I would like to hope it is coil itself but I can't find any confirmation of this.

Therefore here is my questions.

Question 1:

Is changing magnetic flux will create curly electric field and this field will make some charge separation in the coil and hence potential difference / conservative electric field exactly across the coil ?

Something like here: So it means coil is actual place where PD is developed and basically it would be same situation like in the case of motional EMF and rod.

Question 2:

If answer on first question is YES, will this suddenly occurred in coil PD propagate down wires like I described above ?

If answer is NO I would like to know how PD would appears between wires ends / terminals.

Update:

I found couple of animations wich can in some sense show how I imagine this process.

There is gif image of coil in this topic wich show how PD occur between gap when curly e-field appears - Microscopic picture of an inductor

Guess same mechanism can be applied to solenoid above.

And then if we attach wires to gap we got this one in / between the wires - https://upload.wikimedia.org/wikipedia/commons/f/fd/Transmission_line_animation3.gif

Is this appropriate picture ?

Sorry for my english and stupid questions. Thanks for the help.