I think this species would mate just like animals in the wild do, if reproduction is actually necessary for survival. Which means that rape would be the cause of a good percentage of births that occur. But on that note, sexuality in and of itself is objective, so even if you do have emotions and the ability to feel sexual attraction, like most modern humans, when you feel such things for another person, you're still looking at them as objects. Living objects, but objects. Because the desire you're feeling is objective. You have the desire in the first place because there's a reason for it. Some times, it's not even a conscious feeling. You can feel it without even realizing it. Like when you feel attracted to a woman, for example. You think it's because she's pretty? Pfff, hell no. It's because you want to breed. You want to make babies. You may not be thinking of babies at the time, but the function of the desire is still the same. That's why it's called an instinct. You don't know it's happening when it's happening. Like blinking. That's why sexuality in itself is objective. It wouldn't be objective for a species that had no need of it.
If reproduction is NOT necessary and this species lacks much of the things we have, but sex is still possible, I can see them having sex, but only to solve curiosity about it. Otherwise, they may not even have the biological components to have it and will have to stick with what they're capable of, which would more than likely be asexual reproduction. That being said, if they were to see our attitudes towards sex, it might confuse the hell out of them. Imagine you were one of them. What are these things that look so much similar to yourself, but do such weird things? They have to have heterosexual sex to multiply and on top of that, there's all these stigmas they have about sex itself. I think if you were a being that didn't need sex as much as humans do, such stigmas would seem rather pointless. If you were capable of having sex, but it wasn't necessary for your species's survival, you could probably engage in homosexuality and it wouldn't be nearly as big of a deal to other members of your species because sex itself isn't a big deal.
As far as longevity of the species goes, it's hard to say at first, given that this one in particular is supposed to be technologically advanced. Advanced technology would mean this species having more time on its hands and if it eats healthy, exercises a little bit every day, and has suitable medicine, it can live a good while, even without heterosexual reproduction. Having said that, a lot of species on Earth have lasted a long, long time, but some don't seem all that advanced. Look at microbial organisms for example. They've been around longer than, well, anything. And all they have to do is just split themselves to reproduce. But they're also the simplest organisms on the planet. Those that do heterosexually reproduce are far more complex and I think it's because they have to be. They can't just split themselves and be okay. They have to work a little harder than that. There's a bit more of a risk to dying out if they don't. Given that the aforementioned hypothetical species is technologically advanced to about our level or more, they can probably live about as long as we do, but they would have to reproduce constantly for the species as a whole to survive. It's hard to say since our own species hasn't ended yet. We suffer the same threats as other animals if we don't reproduce enough, but we've advanced so far in technology that sex isn't as important as it used to be.
So I can't really say. If sex isn't all that important to the hypothetical species's survival, just as it isn't as important to ours now, the individual could live about as long as we do with its free time and spiffy technology and in theory should have far less stigmas against sex than we do. We only have stigmas because we need boring old heterosexual sex to keep the species going. Something truly catastrophic would have to happen to even put a dent in our species's longevity at the rate we're going. The same would probably happen to this species if it reproduced often enough. Also, if said species is hermaphroditic on top of being asexually reproductive, it would be a lot easier to reproduce. Perhaps a little too easy. They would be multiplying rather quickly, but their average life expectancies wouldn't be like that of a simpler organism, because they've evolved more complex systems and in turn, their technology has evolved. I'm having trouble deciding whether or not this would be the case, however, because sexuality and evolution walk hand in hand. The more complex organisms are fewer compared to microbes and have to reproduce consistently to keep the species going, but are also the more advanced biologically.
I want to say that as an asexual creature, you'd be a lot less complex and there'd be a hell of a lot more of you. I'd be very interested to know how this hypothetical species became so advanced in the first place. I think there's a lot more I need to consider before I decide. There's a lot of contradictory things going on, me thinks. One the one hand, this species can survive for eons if it reproduces enough. Probably outlive us. But on the other hand, it seems that without the ability to heterosexually reproduce, it feels that it would have to be a much simpler species compared to our own. I'm having trouble imagining such a species that looks like us and has spiffy stuff like us, but reproduces asexually. Then again, heterosexually reproductive species aren't that powerful, either. They have to have a steady reproduction rate or they'll face extinction. I mean look at pandas. They're kind of finicky when it comes to sex and now they're endangered.
A highly intelligent species would no doubt develop a system of reproducing to what they believe their optimal level, and they would able to achieve and maintain that for quite some time, assuming they use their advanced technology to do this, until some space-barbarians come about and fuck 'em all up. This leads to, naturally, no form of sexual selection whatsoever. What implications that has for this species are beyond me, as I'm no ecologist.
As for their perceptions of us and the way we think of sex, that is impossible to say from just their reproductive cycle. We also have to consider the individual judging us and the culture from which they hail. Consider for a moment, those who get off to watching animals have sex and those repulsed by it. Their opinions would range from "needless" to "I cannot stop watching this," especially because whatever perversion that an individual has (genetic or memetic) would not be selected for, sexually (unless they develop an ideal individual, and then THAT depends on culture far more than structure of the creature).
How well suited are they to their environment? Because we have no idea what this environment is, we cannot say how long they'd survive.
Related; when you are discussing species morphology, asexual does not mean "doesn't feel sexual attraction," it means "has no gender and reproduces asexually."
Your question is bad, not because it is stupid, but because it is unspecific and lacks the information to answer it adequately.
1. That would work only if the species sees it as economical and widely-available, but asexuality doesn't imply the lack of sex and this species operates on the will to develop technology and specimen preservation without emotional attachment. A systematic approach could be likely for this species and technically, this specie would be attracted to the mind.
3.Could be a possible scenario if they don't have much wills to preserve their race.
Alrighty, let's look at this logically. The species would have evolved beyond physical sexual attraction in favor of intelligence. They would not be attracted to each other's bodies, but their minds. If they are asexual, then reproduction by conventional means would be ineffective without the biological reaction to sexual attraction. So synthetic reproduction would be used. Whether or not this would mean artificial insemination or breeding fetuses in a lab depends on the species preference of whether or not a female's ability to bare children would be a genetic aspect they would want to promote or if they would want to grow them in a lab where constant monitoring and modification would be easier.
As for how the species would get to this point. Well, given that their bodies have the ability to reproduce heterosexually means that they evolved from a species that had sexual attraction. Before intelligence became the most desirable trait and their existence became dependent on technology. Otherwise, their species would not have made it past the fledgling years if sexual reproduction didn't come naturally to them. Then, as technology became a cornerstone of their race, aspects like physical prowess would become less describable against intelligence. Thus, being sexually attracted to the body changed into attraction to the intellect.