Management does not affect anything for NPCs, as it's the PC's Management skill that matters.
Medical Skill matters for the NPCs involved in a Cybernetic Installation operation.
Strength and Dodge are related to Combat and will of course affect combat actions in the circumstances where those are possible.
Speed affects movement, so yes it does make a difference anytime the NPCs are moving.
Speed, Strength and Dodge also are integral skills as part of the A/E rules
, and make a difference accordingly (along with the other related skills).