Primitive and crude mean the same thing. They're synonyms.
Primitive has a base in the word "Primate", so something that is more primitive is something more unsophisticated or savage.
Yes, spices were grown in primitive agriculture. Sure, if by primitive agriculture you mean horticulture, seasoning plants definitely count as primitive agriculture, supplementary to hunting and gathering.
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There is no such thing as primitive science. The same laws of science apply today as they do for yesterday and tomorrow! The word science really means 'knowledge'. Most of the time we use the word to refer to the specific methodologies and systems that are involved in experimental research. So Primitive Science can mean 'primitive knowledge'. See link.
No facility is a place and equipment is anything kept, furnished, or provided for a specific purpose.
Facility as a noun means a building where an event can take place or an activity can be performed, such as a sports facility or a meeting facility. As a verb, it means the ability to adapt and learn quickly.
No. Early scientists who first examined the platypus assumed that, because it lays eggs, it was primitive. More advanced scientific methods since then have indicated that the platypus is not at all primitive, but highly developed. It is one of the earliest known species, and one which had hardly changed from its earlier form, but this does not mean it is "primitive".
Considered by whom? What do you mean by the terms "primitive" and "civilized"? The word "primitive" may have a meaning if you put it in a specific context; "civilized" is such an emotionally loaded term that you're better off not using it. A community can be technologically "primitive" while adhering to a highly "civilized" mode of conduct.