If the fittest die as well everything's dead, so no more life.
Not sure what you mean by evolution being slower without intelligence. I'd expect the opposite. Intelligence means you can adapt to your environment behaviourally and technologically, instead of biologically so natural selection becomes less of a factor.
Second, the chemistry of life balances on a particular set of characteristics:
1) Water is an extremely unusual molecule. It has much more varied reactions than just about any other solvent. This puts life in a particular temperature band.
2) Carbon chemistry is very energetically favorable relative to the other options. Binding energies are close enough that swapping around carbon, nitrogen, oxygen and hydrogen atoms doesn't take excessive amounts of energy.
3) Carbon, Oxygen, Nitrogen, and Hydrogen are all relatively close to one another in size as well. While carbon chemistry does borrow from higher in the periodic table, that tends to be the exception.
While intelligent life will likely be completely different from us, it's very likely that the underlying chemistry is going to be very similar.
The interesting question will be whether we have exactly the same basis DNA pairs. There has been recent successful work to synthesize new "unnatural" base pairs which can then be replicated in organisms.
That said, have you every thought of how alien intelligence might look that does not adhere to the above chemistries?
There are some great science fiction speculations - life living in the ultra-high-gravity "crust" of a neutron star [0], intelligent Turing machines running in the convective layers of brown dwarf stars[1], just plain bootstrapping an AI environment on the substrate of the Universe.[2]
[0] Robert L. Foward, Alystaire Reynolds [1] Stephen Baxter [2] Greg Egan
4) "Room temps" are really comfy for using enzymes to perform energetically infeasible reactions. Too cold and life is too slow to survive and much hotter and you get thermal decomposition faster than life can grow. Its chemically universal... we have the technology to do o-chem and biochem under much weirder conditions than where it actually works best.
5) Trace elements. Despite huge evolutionary pressure and no small amount of experimenting with blood chemistry we're still stuck with red iron based blood. Imagine if you could make blood out of pure protein or even just carbohydrates... But no, every red blooded animal on the planet is stuck refining bioavailable iron, no matter how much of a PITA that is. Would not be surprised if space aliens bleed red like us.
6) Water is awesome for buffer chemistry and this feeds back into your point #1 and my point #4 but homeostasis in the blood or innards in general would be nearly impossible under any other chemistry.
I would not be surprised at all if space aliens were quite familiar with hemoglobin, chlorophyll, some of the cycles like the Krebs cycle. Krebs is very complicated and PITA but most earth life depends on it because it works, if something better were possible, it would have gone extinct half a billion years ago... It would be a fun race, seeing if human and space alien physicists or biochemists start communicating first. My money is on the biochemists, more shared background.
I would still hazard a guess and say that I would expect carbon based life to be there basis of the lions share of life in the universe though.
Regarding the Krebs cycle and other biological feedback cycles, I strongly disagree.
It came to dominate at a point where it propagated through all the extant branches of life, but it is by no means the only way life could have decided to do the process of energy production. Once evolution evolves something, it is stuck with that system - no complex biochemical system will evolve into a Krebs replacement whilst Krebs occupies that niche, and evolution isn't going to spit it out of the way!
Careful, this isn't a given. Some tunicates actually concentrate vanadium for oxygen transport.
Now, iron is so much more plentiful in the universe that it's likely that it would be pressed into service for oxygen transport, but it isn't given.
In addition, life looked very different before the Oxygen Catastrophe, so we have lots of evidence for life without oxygen transport.
Is there a firm distinction between "alive" and "dead" at all? I think not so much. What we call "dead" is a body whose micro-organisms no longer organise in a common human perceptual window of space and time. With a microscope, some people have been able to see that a "dead body" is actually buzzing with life. Many of the same organisms that live symbiotically with us survive the immediate death of the eukaryote body and pass memories of our memories on to future generations of micro-organisms. They are (usually) symbiotic with, but not dependent on, as the organelles of "human cells" have become, our larger organising bodies. What happens as these wild bacteria and fungi unpack and metabolise our memories on the deepest level? Is that not somehow part of the life cycle? Isn't it possible that "we" somehow experience that in a less integrated way? Poetically, as the inside members processes the death of its larger body, so do the exterior members of the human body, other people, animals and social organisations. The locus of stable control is released, the steering wheel disintegrates. But does life somehow "disappear"? Not at all. It only shifts in, out, to scales whose feedback mechanisms elude mainstream western mythology.
Eventually, over thousands of years, all membrane bound creatures deposit their bodies. What went in (the membrane) must go out(side of the membrane). Some parts are reused immediately. Others are left for deeper cycles (including by not limited to eventual metamorphosis in the high pressures of the deeper subterranean). This part of the life cycle is much more mysterious to me, as I haven't really studied it, and it really is so much more vast. The physics and chemistry of rocks and minerals, liquids, gasses is part of the life cycle. They are part of the evolutionary story as much as any being.
Why are many mystics attracted to crystals and rocks? Because they are mineral deposits of ancestral beings. They carry, literally, the energies accumulated in some ancient, swirling ecosystem. They are a memory of things our bodies had forgotten. Same reason why a lot of scientists are attracted to them.
As for the conversation about "intelligence". The Earth has 400 billion trees. Each is connected to the others by roots, by air, by micro-organisms, by water, by chemicals, by ecological relationships. How many neurons do we each have? Maybe 80 or 90 billion.
Just because plants can't move or talk in very specific human babble noises, it doesn't mean they aren't experiencing something substantial or contributing in dynamic "intelligent" ways to their ecologies.
Anyway, I need to take a break and eat lunch, because I'm "alive" in this certain kind of way where that my fire is burns for tasty food. I'm gonna stoke it with some soup.
Edit: I can't reply to your reply, but I can edit this post. Unless the form that mate selection takes radically diverges from evolved patterns I don;t see how that makes much difference. Since survival for intelligent species is much more loosely coupled to their biology I don't see why sexual selection strategies would mitigate against that. It seems to me they'd follow the same pattern in devaluing biological fitness criteria as not being as significant as they were pre-sentience.
I'm quite certain that does not have anything to do with "speed of evolution".
I am not a biologist, so I can't come up with a better source, but I'd suggest that everyone would very carefully study at least the Wikipedia article https://en.wikipedia.org/wiki/Evolution which looks like a reasonable summary.
I'm not sure what are you saying here. The "fittest" are the ones who don't die (before reproducing).