Again, you are treating the concept "survival of the fittest" as "the truth, the whole truth, and nothing but the truth", when it is nothing of the sort.

If you've seen experiments demonstrating the Leidenfrost effect, you'll know that it is quite easy to make water run uphill. Does that mean that gravity doesn't exist? No, it just means that gravity is not the only force that is in play.

Evolutionary processes are themselves subject to evolution. In other words, evolution itself evolves. Over time, basic mechanisms give rise to more complex mechanisms which partially or wholly subsume the functions of the underlying ones. This does not mean that the basic mechanisms disappear, only that they are no longer the only things guiding the evolution of an organism. Sometimes, different mechanisms end up working in opposite directions.

Additionally, evolution does not work exclusively on one specific level, but rather on all levels at once. Yes, it works on species as a whole, but it also works on individuals. It also works on groups of species, from two specific ones to whole ecosystems. It does all of this simultaneously and without cessation.

A classic (and often completely misunderstood) example is the "female's choice" mechanism. This is often used as an argument against "survival of the fittest", when in fact it is quite the opposite. SOTF seeks to maximize the survivability of both the individual and the species (and the two are tightly connected). One way to ensure that the next generation of a species has the highest possible level of survivability, is to attempt to restrict breeding privileges to the strongest members of the species. As such, from the point of view of the species, there is a clear evolutionary benefit to females being picky about who they breed with. However, this requires that the females use some sort of selection criterion that they are able to gauge with the senses they have available. In the case of many species, this has resulted in females being rather drab-looking, while males have some sort of spectacular coloring or other extreme physical appearance. As long as the survivability of the resulting individuals is good enough, this mechanism can keep pushing the males' appearance to further and further extremes, even to the point of actually lowering their survivability.

However, evolutionary mechanisms are as much effects as they are causes. Evolution is a difficult subject to discuss, because our thought processes and languages are not well equipped to describe the concepts involved. We tend to think in terms of causes and effects, of things happening in a linear fashion, one after the other, and our languages reflect this. In terms of evolution, everything happens at once, and everything affects everything else to a greater or lesser degree. Each element you focus on is not either a cause or an effect, but rather both a cause and an effect.

tl;dr:
One, what has to survive is both.
Two, "survival of the fittest" does not mean "the bestest evar", it does in fact mean "good enough".