Fate:

I looked it up and found something called the Fate SRD, which I am assuming is at least similar to some edition of Fate. Assuming this is the case, it seems like it could work for the setting; however, the mechanics seem very foreign to me. If I were to run a game using this system, I would definitely want to get a printed copy of the rules and read it thoroughly.

It is certainly interesting, however.

(By the way, the way I would have magic work is to have it not really be different than other forms of activity; doing certain things would be strenuous much like lifting a heavy object physically would be, for example, while easy tasks would not tire one out at all.)

To my knowledge, no such translation exists.

Judging from your descriptions, you're still looking for a p&p with quite a lot of crunch; did you ever think of trying a much more simplified system? It doesn't have to be 'zero crunch' FATE, but how about the rather simple "Mutant: Year Zero" and "Coriolis" systems?

...they would have to be adapted to your setting quite a bit, the talents in particular. And you could not use the fluff at all. :|

Why wouldn't D&D work? Systems like that and Pathfinder are incredibly flexible to work with House rules and custom setups.

Yeah, the actual game part of Fate is designed almost solely to facilitate story-based roleplaying. There are no stats or attributes; just descriptors positive or negative dice. It's great if you want to drop the crunch and try something different. Fate Core is a fantastic book to start with.

But I'm thinking it still won't quite fit.

As a lot of others have suggested, Savage Worlds might be a nice fit. I've run a variety of games in the system and it's very modular, with a good powers supplement and easy building of new races. The combat engine is the only thing I'm not a fan of. It's designed with minis in mind but I've never used them and had no issues, my problems stem from the way it uses the first blow to stun characters and how it drags combat down to make checks to get back in the fight, so next time I run it I'm house ruling that aspect.

Otherwise, it offers great adaptable crunch without the nightmare mess of startup that GURPS promises...

Savage Worlds:

Looking at the Wikipedia article for a summary of the system, it seems like it could fit. Perhaps some of the normally mundane skills could be treated as magical in this setting, for example (but still work the same mechanically). The whole notion of race sometimes representing something like nationality suggests that using it to represent species in a no-human would could work.

One oddity with the "Acing" mechanic: A character with a low score in an attribute is more likely to ace than one with a high score. I suspect that this may have counter-intuitive results, such as extremely difficult challenges being more likely to be performed for less-skilled characters than more-skilled characters. Has this quirk of the system ever led to strange results in actual play?

Besides that with some houserules D&D 2-3.5 would be fine you give a pretty close description of the "Fading Suns" RPG setting. Its all about alien worlds, lost & found ancient technologies, mysterious mental abilities etc. I read a lot about the setting description but have not played it so I'm not sure how good it is.

https://en.wikipedia.org/wiki/Fading_Suns

That could work. The arcane skills work the same mechanically as the others anyway - you roll your Spellcasting/Faith/Psionics/whatever to use a power just as you roll Tracking to follow a trail, Lockpicking to pick a lock or Fighting to hit someone. Another option would be for each spell/power to have its own separate skill rather than a single arcane skill - that's how one of the standard arcane backgrounds works.

In my experience it works fine - any such anomalies are rare and minor enough not to discourage anyone from increasing a trait from d4 to d6, nor even to be noticed unless you're looking carefully for them. The probabilities have been discussed on the publisher's forum; I can't find the relevant discussion, but IIRC the conclusion, supported by calculations of probability, was that any such anomalies were minor, only occurred in specific mathematical situations (where there was a particular penalty to the roll) and in any case are mitigated in most important cases by the wild die (always a d6), which all player characters and major NPCs roll alongside their trait die and take the better of the two. So it's not something to worry about.

I don't have my books at hand, but from personal experience I never had that sort of issue. The exploding die mechanic allowed for some awesome feats of heroics, making it good for a high magic game, and it never seemed to encourage making weak characters to game the system as your odds of success greatly improved once you became skilled, because otherwise you suffered a penalty.

Also, a d4 exploding isn't going to help any but the most trivial tasks, as you would have to get at least two explosions to add up to anything worthwhile.

In my time running it for pulp action/adventure games, the only major combat hurdle, as I said, was the stunning of any character who took a hit. That stunned character then cannot react until they succeed on a roll to put them back into the fight, and that can make slugfests drag.

But the system does play fast otherwise, requiring very little rules lookup. And I loved the card-based initiative so much that I've basically used it in every game I run, from D&D on down the line, with only a few modifications.

GURPS:
Does seem like it could work, but isn't without its issues.

One in particular is that the TL system assumes a linear progression (so a setting with computers but no firearms, for example, wouldn't fit) and doesn't seem to lend itself well to the ancient ruins case. In particular, I note that the case of a character finding a modern weapon while adventuring doesn't work well; the character will not likely have the skill to use it, and the character's TL would be way too low. In a game where you only get a few points per playing session, having to spend dozens just to use that shiny new tool you just found seems to be a bit much.

Also, having played Daggerfall and Battlespire, I note that a disadvantage system could lead to overpowered characters if you're not careful.

On the other hand, the magic system seems (at first glance) reasonable, and the rules for races also look decent. However, the GURPS Lite rules limit natural tough skin to what it considers human levels, which might not be appropriate for an alien fantasy world where some races might indeed have tougher skin (and might have limited armor selection to compensate).

Time Cube RPG:
Seems really strange, and not the sort of thing that would work for even a somewhat conventional game.
One thing I don't like is that the rules enforce the gender binary; one houserule I would use (if I were even to attempt to run this strange game) would be to change that.