I will give my understanding to this and a couple of links that may help you.
Regarding how they overlap:
I have always viewed this as the two worlds (material and shadow) exist in the same place at the same time. So if you Move through the gauntlet either way you end up in the same location you were but in a different place of existence. Therefore in areas where the barrier between them is weak you can have entities interacting with items that are simultaneously in both realms.
Also items that have existed in the material world may still exist in the Shadow. As WOD wiki puts it:
"anything of import that happens in the Material Realm may birth a reflection in the Shadow".
I take this to mean any things that have strong emotional or reality changing consequences attached to them. Examples: a child's lost Teddy Bear may still exist in Shadow realms, had strong ties and was of great import to that person, or a declaration of War that lead to the deaths of many and changed world events. Even if destroyed in the material world a spiritual copy may exist in the shadow.
"Thus demolished buildings, ancient trees and extinct animals may all still exist there in spiritual form" http://whitewolf.wikia.com/wiki/Shadow_%28WOD%29
how the Uratha are able to interact?
Uratha can speak with spirits, if to a very basic level.
"They [Uratha] also possess an instinctive (if rudimentary) understanding of the First Tongue, the language spoken by their ancestors and still used by spirits (it is possibly also the original language of all humans). Many Uratha learn to speak the First Tongue fluently. " http://whitewolf.wikia.com/wiki/Uratha
what motivates more complicated spirits?
The same things that motivate other NPCs in your games: power, wealth, charity, compassion. They are just NPCs living in a slightly different world. They can have motivations as varied as any other group/individual.
what they would know?
This is for you to decide, some may know ancient lore, they may communicate regularly with creature on the material world (How up to you), others may know very little about anything material or shadow, this is for you to flesh out and make appropriate for the plot. Would likely depend on the power/rank of the spirit.
how they interact?
Usually via a point of low strength in the gauntlet, or by forcing through it.
With what each other? I imagine like we would interact in our world. Write a letter and send it by messenger. Meet up in a location and talk or fight or conduct dark rituals to bind the souls of mortals to their eternal servitude? Again up to you. Or conversely do a binding ritual to stop their evil brethren destroying nature. Similar spirits are likely to be found together in 'choirs'.
With your party? At a site of weakness in the gauntlet, or where they have been able to force their way through. Or it could be they cannot get through but have the means to cause a burnt scrap of paper to fall at the feet of a player, or cause the group to hear whispered words in the dark. Or it could be your players that set out to contact a spirit to help them, get a message out to someone else while they are in captivity.
The contact and interaction could be initiated by either side.
when would they interact?
Again really up to the party or you.
how much do they move around?
In the shadow realm, I have always thought of walking or riding spiritual creatures, such as a spirit horse or spirit elephant, in these cases bound to the service of another spirit. It depends on the type of spirit.
An animal spirit would move as that animal moved. A tree spirit would likely be rooted to the spot. You may wish to embody spirits in things that evoke the thing they represent. So a wrath spirit may be a floating ball of bale fire, that levitates, or a spirit of the meadows may move as a swirling cloud of flower petals. This would not mean that the Wrath spirit is necessarily evil and the meadow spirit happy and bright.
In the material world? it is up to you if they float as disembodied heads, or the wolf spirit hunts around the shadows. They can only interact with the real world through their powers, so pass through real world objects as if they were air.
Again much of this is up to you but I hope this helps you flesh out how you are going to envisage your spirit world.