What makes people easily subscribe to pseudoscientific theories? There are many theories/disciplines that have been categorized as pseudoscience in the scientific community.
The list includes many things that are regularly even quoted in media like graphology, astrology, psychoanalysis, personality types, etc.
Questions:

What attracts people to such theories? Do any cognitive biases make people believe them easily? Which part of pseudosciences acts as a stimulus that triggers this cognitive bias?

If there's a cognitive bias behind people believing in pseudoscience, knowing that a majority of the population does that – is there any term for such a phenomenon in social psychology?

A majority of the population believes in some kind of pseudoscience. Does this signify an evolutionary aspect of our minds – that people are still evolving into better species that might one day believe in proper science? Pseudoscience seems to be older than science; correct me if I am wrong here.
There are two great TED talks that together help shed some light on your question:


David Deutsch (2005) "A new way to explain explanation", and
Richard Dawkins (2009) "Why the universe seems so strange"


At a fundamental level, science is about explanation (and sometimes using that explanation to make predictions). Thus, to most people, science is useless unless they understand the story it tells. The problem with modern science is that to have a good grasp of its explanatory power, you need a lot of (often difficult) background. As you gain this background, you develop what Feynman would call the most fundamental skill in science: always questioning, being able to say "I don't know", and to hold contrasting ideas together. If you don't invest in acquiring this background, most of science seems like witchcraft passed down by ivory-tower academics in funny gowns and hats. 

What pseudoscience (or even cargo-cult science) provide is explanations that require less background, purport to be more certain, have something for everyone (Forer effect), and reassure you that "there is an answer". If you look at much of pseudoscience (or ancient myths) more closely, you will notice that they tend to personify their subject matter much more than science (my favorite example is the homunculus fallacy). They use this personification to provide agency, intent, and meaning to their explanations.

The great advantage of these human stories is that our minds are optimized for them. If you subscribe to Dunbar's Social Brain Hypothesis, then one of the main things evolution produced is a mind built to understand social structure, and other people. When an agent does not adhere to its role and violates our theory-of-mind and behaves erratically, without discernible intent and meaning, this is dangerous to us and our society; it causes us great discomfort. When you hijack the social mind to try to explain further and further afield parts of nature, you try to build the same sort of characters. 

When you have to say "I don't know" or "I don't understand" this character, it creates discomfort. Pseudoscience thrives on this by giving an arbitrary, simple, shallow and easy to change explanation. Since most lay-people never pursue this explanation far enough to notice its contradictions, and since it shapes their observations (in the Popper-sense and through confirmation bias) they never get a strong enough cognitive-dissonance to overcome to positive feeling of having an understandable 'explanation'.

Unfortunately, all I can do in this answer is provide a intuitively appealing, intent and agency based explanation. Reread my answer and make note of unnecessary personifications I made -- just like much of pseudoscience, science is a story and there is the biggest rub.