A science has a scientific method, involving falsifiable claims, experiment and observation, and reproducibility of results. A scientific theory is not the same as fact. It is not an explanation that has been proven, but rather one that has yet to be disproven and that explains all available observations. This distinction is important. To the extent that psychology employs this method, it can be considered scientific.
This itself is suspect. Psychology is the red headed stepchild of the natural sciences.
Not that I agree with Mole. His reasons for saying the Psychology isn't a science are wrong. But the general claim is up for debate. You yourself said that the scientific method relies on experiments that involve observations.
There is no reliable method of this in Psychology, and therefor Psychology is not reliably a natural science. You can only observe behaviors, and even behaviorism has evolved away from being solely behavior-based.
Psychology is the study of the mind. If you study only the brain, you're in Biology. If you study behaviors, you're studying only half of the subject matter. If you study thought and emotion and human consciousness, you're out of the territory of observation and out of the territory of science. At that point you're into philosophy, which I personally think is the better classification for a large portion of psychology, I'll mention that below. The only way we can study thought and emotion is through self-report, and the only thing in the early 20th century that got Psychology any science credentials was its transition away from self-report as data collection.
Does Psychology need the scientific method? Yes, it's what keeps us from doing lobotomies and hooking people with schizophrenia up to car batteries.
Is Psychology a definitive science? I won't answer that because of the shitstorm that could happen with psychotherapy insurance coverage and our access to science conventions. You don't answer this question out loud just like you don't say the name of the man who tried to kill Harry Potter. In the current academic culture, science is respected and philosophy is not, despite the fact that any Psychology involving thought rather than behavior is firmly founded on philosophical bases rather than scientific ones. But again, psychologists wouldn't get even 1/4 the respect if they were philosophers rather than scientists, so I won't say it's not a science. I will say that if the physicists and the geologists ganged up on us tomorrow and kicked us out of their clubhouse then I wouldn't be surprised.
And lastly, biology was understood without natural selection until it was discovered by Charles Darwin. And now biology makes no sense without natural selection.
Again, you have things backwards.
If I taught someone natural selection when they didn't understand Biology, it would make no real sense.
If I taught someone who knew nothing about natural selection how a cell operates, it would make real sense.
I went to a private Christian school where we were taught natural selection for a single day. The rest of Biology made sense, and continued to make sense with that hop-skip-jump over Charles Darwin. Biology is the study of anything living. Natural selection is the biological sub-study of how time affects the gene pool as well as the resulting biological implications of those effects.