My rim exploded inflating on an automatic pump of a gas station. Should I reuse wheel's spokes/hub or buy everything new?
I don't know what kind of air pump you were using at the gas station. If it was a manual one with just a pressure gauge attached, you can usually use them if you are careful enough.

Automatic air pumps, however, usually have the habit of using this three step algorithm: 1) open the valve to fill some air for a fixed amount of time, 2) measure the effect, 3) correct the error. Problem is, that step 1 is adapted for car tires with their immense volume, so it will over-inflate the tire if the pre-pressure from the pump is high enough. Typical pre-pressure from pumps seems to be around 100psi (my experience), but it can be anything. If your tube has a dunlop valve, that extra pressure will remain in the tire. So, don't use automatic pumps, especially not with dunlop valves.

That said, your rim has a maximum force that it can withstand. And that's where it gets a bit complicated:


The maximum force that the rim can withstand reduces over time if you are using a rim brake on that rim. It's not just the brake pads that wear away, it's also the rim. Give it enough wear, and it will even explode at its originally rated pressure. I'm not sure whether that's the case with your rim, though.
The force the tire's bead exerts on the rim depends on both the pressure and the width of the tire. The wider the tire, the more the tire will tear on the rim's edge. Your tire seems to be of the wider kind, so, even if the rim could bear a slim 100psi tire, 100psi with your wide tire may have been too much for it.
The force on the rim is independent of the tube. The tube is not designed to withstand any forces, the only force that it exerts is the pressure of the air. Whether the tube is folded or not does not change this pressure. So, the opinion of the second bike shop seems to be wrong in this regard.




So, what does that mean for repairing your tire? Well, obviously, you need a new rim.

Looking at the damages to the rubber covering the bead, I would have trouble trusting the bead to remain seated: I would think that the rubber between the bead and the rim does help keeping the bead in place. Without that rubber, I would fear that the bead might have an easier time slipping over the rim. So, I would replace the tire if I were you.

Regarding replacing the rim/tire/tube vs. just replacing the entire wheel, it's a lot of work to rebuild a wheel. If you don't do that yourself, buying a new wheel should be cheaper unless you have a sufficiently expensive hub like an internal gear hub to set off the expenses for work time.