“Some” is restrictive. “Some” applies to particular parts (or part) of the whole, in distinction from the rest belonging to the whole.
Yes, you can say “They don’t have some (important car) part(s)” (...to finish the job; they have all the other parts necessary).
“Do you have some boyfriend?” would be odd, but if you continued, for example, “…over there?” it would be grammatically possible, however risque, because “some” would show its restrictiveness: e.g., one boyfriend over there, another here...If that’s your intended meaning, you could put “some” to work for you this way.
“Do you have a boyfriend?” would be a normal way for a mother to ask her daughter how she’s doing in the relation department: do you have any?