These are the explanations to the examples from the Contrasting Cases blog post.
To increase the speed of an SN2 reaction, the energy of the transition state needs to be lowered. In the first reaction there is no additional stabilization, but in both the second and third reactions the adjacent pi bond allows for delocalization to lower the activation energy. The oxygen in the second reaction is electron-withdrawing, so it increases the speed of the reaction further by making the carbon more accepting of the negatively-charged ethoxide nucleophile.
The fluorine substituents in the trifluoromethyl group are electron withdrawing so the carbocation in the tertiary position is less stable than the secondary position.
The adjacent phenyl ring stabilizes the carbocation through resonance delocalization. Draw all the possible resonance structures for bonus points!
The enolate structure with a double bond to the bridgehead carbon would not be able to form as it cannot be planar.
Concept-Oriented Task Design: Making Purposeful Case Comparisons in Organic Chemistry
Nicole Graulich and Michael Schween
Journal of Chemical Education 2018 95(3), 376-383