ok for the first one, there was somewhere a very detailed post on what exactly each dmg type does, i'll try to find that for you (as i myself only know maybe half of it cough)
But basically the special dmg types dont get affected by your stats but the other way around. So you only can get them by dragon shards or skills or buffs, but they dont only do dmg but also have some other effects (which is explained in the thread i'll search it up) Each respective speacial damage type aslo hase a speacial defense type , while magic damage and physical damage get blocked by magic defense and armor.
Magic damage and physical damage is your standard damage type, based on your class and which actually is based off your respective stats. (and your weapon)
The spirit shield is actually "invisible" in number, but you can see it when you look at the icon of a monster, there is a bar next to them that represents their spirit shield. When the shield is down you can then stagger them for a period of time, until the shield recovers again (yes, it doesnt stay down). Now there is difference between normal mobs, which take sometimes only 2-3 hits and the shield is gone, and elites or even boss monsters. Those take way more hits to reduce the spirit shield, and you only have a few seconds of staggering once its down.
So weither you want to use that skill is up to your playstyle, i myself usually dont look at the spirit shield, you can also kill them with the shield up
Hope i could help~
Edit: found the thread, but it was in german. maybe you want to give it a try anyway: Here
but basically they show how the dmg is calculated on which types. The 2 special effects i remember is Natural Dmg also improving your healing skills (very good for healing oracles) and Dragonspell Dmg having an armor penetration bonus.