Do they have Supervillain(s)?

It's more like making the need for a product and then selling it. That's what Vought was doing to an extent and then Homelander extended it by creating super-terrorists, the Female was also part of that plan.

Also what is supervillain is subjective in The Boys, like are you sure Homelander doesn't count more as supervillain rather then superhero?

Still if we go in full black and white and count The Seven as Naqib can count as supervillain for now.

People have answered your first two questions, so I'll answer the third:

If not, why did the public need and adore superpowered people (Supes)?

A small analogy:

• I want to cut normal trees and I use an axe. I am mildly efficient.

• Someone comes and offer me a chainsaw, I become very efficient at cutting trees. Isn't it enough for me to be happy?

Sure, if there were "super trees" that I could only cut with a chainsaw, the chainsaw would be even more valuable. But cutting normal trees at an increased rate and less fatigue is already something worth of praise.

And that's the same with super-heroes, you don't need super-vilains to make super-heroes useful. You see them resolve crimes in a few seconds that'd have taken hours for the police to handle without any casuality on the "good side". And that's only the logical side of it.

Take also into account that they are beautiful/handsome, have incredible super-powers and most people even think that the powers are god-given.

When you see what little is needed to become famous in our real-world star-system, why wouldn't we revere someone that actually saves people and have real powers?

(And add on top of that a shitton of propaganda from Vaught)

We have seen attempts to create 2 supervillains already but no US born supervillains, maybe that's what you mean. I think this is probably for a number of reasons.

1. Vought pays them; even the low level sups seem to work at some level for vought so there is less desperation to get money. The ones that don't get paid well probably have very minor powers anyway.

2. Vought chooses them; so they are going into the kinds of homes vought approves of, so maybe not areas with a lot of poverty and crime

3. Vought probably keeps an eye on them and steers their upbringing somewhat and can deploy resources (eg a scholarship or a mentor) where required

4. This is complete conjecture but maybe they kill some of them if they seem them going off the rails.

The Heroes and Villains in the Boys are manufactured and both exist

In most stories involving superheroes they just exist, often for reasons unknown (or, at least, reasons unknown to humanity). Humanity doesn't have much say in where their powers come from. They are often accompanied by super-villains with similar origins. Sometimes we get a hint of their origin (modern stories tend to give some clues about where their superpowers originate like those in the MCU where many are aliens or for superman, for example). The important point is that their existence has some external cause unrelated to humanity. And many stories seem to assume that the universe has some balance where super villains also arise (and good stores thrive on conflict).

The "heroes" in The Boys are not random, they are created by people for a purpose. Vought has been experimenting with serums used on mothers/children to create a breed of heroes. They do this because it fuels a huge, profitable hero industry. They pretend the heroes are sent from god or some cosmic random process, but that is a lie.

Initially at least they don't need to create super villains (there are plenty of real-world, non-super bad guys to keep the heroes apparently well occupied). Of course the "heroes" are neither very heroic, morally upright or competent. In one sense the 7 are the bad guys (the super villains of any more conventional story). But, as we find out during season 1, Vought does feel the need to create visible super villains to enhance the role of their "heroes" in the fight against terrorism. They use the same technology that created their heroes and give it to terrorists to improve the incentives for the military to incorporate the "heroes" into military action, something they were resisting at the start of the story (Vought also uses blackmail for this goal, but the existence of superpowers villains is a strong extra incentive).

So, yes, super villains do exist in The Boys and they are a part of Vought's plan to make more money from military contracts.