In response to this part:
If modern humans are the result of mutations in genes, how come no one species over the course of hundreds of millions of years has been fit enough, or advanced mentally like we have, or even in any slightest bit?
All animals are the result of evolution, which includes mutations.
Now, what you should understand is that evolutionary changes have to be selected for, but also must be immediately useful to the organism if they cost more.
There is a long term tendency in our lineage towards increased brain sizes. Animals -> Mammals -> Primates -> Humans. This long term development need not have happened in the first place. In the Jurassic Period, the most successful group of animals were dinosaurs, who in general had small brains.
In addition, our brains require far more calories than the brain of, say, a chimpanzee. Even if you have a lineage that, over the generations, has a tendency towards larger brain sizes, it would also need to be able to hunt or forage more in compensation for the increased caloric needs. If it were not able to do so, a larger brain would actually be a profoundly negative characteristic, a useless drain of energy.
In addition, the benefits of increased intelligence are highly circumstantial. Consider if you gave a cheetah all the brain power of a human. It might then understand that if it dug a hole and placed fake grass over it, it could catch an antelope for less effort than having to stalk and chase it. Less effort means less calories expended and ultimately most of an organism's fitness has to do with how much energy it expends in trying to procure energy (calories).
But lacking opposable thumbs and hands with digits, it would be unlikely to accomplish such a thing. Also, such tasks are more efficient when done by a group, but many animals do not coordinate group-wise as extensively as humans do. So what we have is at least 3 but probably many more things which all have to come together in the same species for them to rise to the top of the food chain like we did:
- Dextrous limbs (i.e. opposable thumbs and seperated digits)
- Brains tripled in size (relative to other species of ape)
- Behavior of extensive group coordination (tribes)
As you can imagine, a species evolving our intelligence and using it to dominate the local ecosystem as extensively as we do is therefore a rarity.