whoa. lots to cover here.... hmm. okay, here we go....
We know next to nothing about the inner workings of stars, much less how likely (or unlikely) rare core arrangements occur. that being the case, we look to akham's razor. there is not reason in physics why 2 cores that behave like a fluid (plasma to be precise) would retain seperate and distinct boundaries while maintaining a unified and cooperative co-arrangement. my analogy still stands: when you throw a cup of water into the ocean, you never see a cup-shaped chunk of water floating out to sea. they merge and become one structure. since we know so little about the inner workings of a star and nothing about their core, the structure could take on any number of forms. however, thru your wording you make it sound as though the two cores would be effectively indestructible and instead of joining into one system (with any myriad structure arrangement), would remain seperate yet joined in close proximity. even basic physics calls this an impossibility. when two stars collide (no matter what 'speed' they are moving toward eachother at) they always explode; in that their structures are torn apart and scattered in the local area. they eventually coalasce into a single star. if i take two cars and grind them into chunks the size of a postage stamp and then throw them into a ditch, i dont get a fully formed vehicle with two distinct and whole engines under the hood. this applies to stars as well. no part of a star is solid, so when a star is torn apart, the core goes with it. the core of a star is simply an area of plasma that is under different temperature and pressure tolerances, nothing more. the name "core" does not denote a firm (solid), material object but merely defines a boundary. there is no such thing as a star with two cores, period. stellar cores cannot migrate cohesively in the process of a stellar collision.
comets can be captured and are not entirely ice and gas. several moons of saturn and jupiter are thought to be comets. comets are a fact of existance in the universe and do not "go away" or even "lessen" over time. there is no speed limit for comets. the only thing that distinguishes a comet from an asteroid is that asteroids are typically more metallic than rocky. comets are typically composed more out of an aggregate of metals, rock, frozen gas and ice. a few thousand miles per hour makes little difference when something is hurtling thru space at 40,000 mph.
the orbits of the planets in our solar system vary greatly. pluto oscillates at up to a 30 degree angle from the solar plane. uranus sometimes does at up to 18 degrees. all the planets in the solar system have "irregular" orbits in that none of them would lie on top of eachother if you stuck them all the same distance from the sun. the earth does this as well. there is no such thing as a perfect orbit. all orbits are elliptical. that is a scientific fact that most highschool science teachers leave out of the lesson plan. those that say that the 'default' orbit type is a circle are uninformed, uneducated, ignorant or just plain silly. circular orbits can and sometimes do occur but only in specific circumstances and never in a solar system with a single star and multiple satellites.
gravity can shape planets of larger masses, but moons are often shaped largely by impacts. since smaller celestial objects often lack sufficient mass to properly "smooth" the surface or correct for areas of varying density, they are often left misshapen.
