Unless the astral changed from the 5th edition::
do they only work on the astral plane?
Mana spells work on the physical plane (against living targets that have an actual physical body, like materialized but not manifesting spirits, guards, magicians using astral perception etc) and they also work on the astral plane (but only against living entities that have an actual tangible astral form, like spirits, magicians using projection or perception etc).
Physical spells only work on the physical plane. They work against living targets with an actual physical body (such as a guard or a dog). Some (for example indirect combat spells or improved invisibility) also work against inanimate physical targets (such as a drone or a camera).
Can they affect a spirit that has manifested in the physical realm?
Spirits always have an actual tangible astral form on the astral plane and they can always be targeted from the astral plane (but only with mana spells).
A spirit that manifest does not actually have an actual tangible physical body on the physical plane and cannot be targeted from the physical plane (you need to use astral perception or astral projection to hit it).
A spirit that materialize have an actual tangible physical body (in addition to its actual tangible astral form, it becomes dual natured) and can be targeted from the physical plane (with both mana spells and physical spells)
Can they affect a living mundane person who can not project or perceive astral?
While intangible living auras can be sensed when using astral perception, intangible living auras alone cannot be targeted.
If you are a wholly astral entity (such as a spirit not using materialization or a projecting magician) then you can only affect targets that have an actual tangible astral form (spirits, magicians that are using either projection or perception etc)
If you are using astral perception then you have an actual tangible astral form which mean you can affect other entities that also have an actual tangible astral form (such as spirits or other magicians using astral perception or projection), but in this case you also have an actual tangible physical body (you become dual natured) which mean you can also affect wholly physical targets that does not have a presence on the astral plane (by for example physically touching them).
And do physical direct spells like Power Bolt only effect living beings on the physical plane or can you shoot a non-living target as well?
Direct combat spells only work on the physical plane and they only work against living targets (targets with an actual tangible physical body that also have an intangible living aura).
Indirect combat spells also only work on the physical plane but since they form actual physical effect (such as a shockwave or a ball of fire or electricity etc) they work against all physical targets. Not just living targets.
Other physical spells might or might not work against inanimate targets. Improved invisibility cast on a living target, for example, will work against drones and cameras trying to observe the invisible target (but being invisible will of course have little to no effect against for example a maglock or a pressure plate in the floor).