ANSWERS: 1
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First of all, the proper term would be lithospheric slab. These slabs are actually mostly mantle material with only a thin layer of crust. Second the iron-nickle alloy that is the core is much denser than the rock the makes up the slabs. Therefore, they cannot sink any lower than the boundary between the core an mantle. Therefore it is unlikely that sinking slabs would be able to affect the inner core in any significant way.
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