I'm a bit unsure about materializing. A spirit needs to materialize to affect something on the physical level, but Influence power is type "M". Does the spirit still need to materialize to use this power on a mundane human?
Yes, as you're naturally physical. See p301 of core.
Spirits are naturally astral forms, much like you’re naturally a physical form. A spirit exists entirely in astral space, with astral attributes equal to its Force. A spirit can manifest (p. 314), use astral travel (p. 313), and get blocked by mana barriers (p. 315), just like any other astral form. Its appearance strongly reflects its type and the tradition of the magician who summoned it. A hermetic fire spirit might look like a traditional fire elemental, while a shaman’s spirit of air might appear as an eagle or a butterfly. If a spirit wants to affect anything on the physical plane, it has to materialize first (p. 314). It gets physical attributes based on its type (Spirits, p. 303) and appears as a solid, physical version of its astral form—it’s relatively solid even if it doesn’t look solid, like a spirit whirlwind or a water elemental. The spirit is dual-natured while it’s materialized, which means it exists simultaneously on the physical and astral plane, meaning it can see objects in both places—and be targeted by both mages on the physical plane and astral entities, such as astrally projecting mages.
Magical effects need you to be on the same plane as the target. See p282
Mana spells: When using mana spells, the magician can only affect living things with auras or astrally active entities (such as spirits or foci) even in the physical world. Mana spells can affect targets on either the physical or astral planes, but only if you’re on the same plane as your target(s).
A mundane human is naturally a physical form, and so they can't use mana spells on them.