Your definition of "factual", and "moral" is not shared by everyone else in the world.
Your "facts" and "morals" are determined by your "belief". The existence of God is a fact for a christian, for instance. Thinking your "facts" are better than their "facts" makes you closed-minded, not open minded.
Determining the plausibility of a hypothesis based on what is currently known is philosophy, not science specific.
To name another subset of philosophy, in theology they also test hypotheses based on what is known, but the procedures, dogmas and axioms are different.
No, facts cannot be changed based on one belief. One can believe in none factual things. No matter a person belief, a proton will always be composed of three quarks. Belief does not trump Empiricism. Please note that I use it in the context of scientific inquiry.
Morals can have subsets of additional values that arise from cultural backing and belief but there is a core morality of human spieces as sociology is discovering, that crosses ages, race, and country cultural barriers. Thusly, moral can be used as a finite word.
Believing in something hard enough does not turn something into a fact. It can be acted on as if it is a fact. This is a key subtle difference.
No, determining plausibility is a wholly mathematical process and as such not philosophical. Therefore it is a tool that can be used by science, my original premise was misstated, excuse me.
In theology, the procedures are baseless and lack rigor for authentication of its conclusion, its a poor analogy.