There things are outside the scope of any written rules, and Paizo is not able to think of every possible situation. That means it is up to the GM to decide. If this is a PFS game I would not use this idea because table variation will give different answers.
As for your armor and weapon question they are do not apply to the other category. One is an "enhancement bonus to AC". So even if you change the armor to a weapon it won't do anything for the weapon's attacks, and the weapon's enhancement is not "an enhancement bonus to AC" so changing the sword into armor wont do anything for an AC bonus.
Ouch... Everything related to magic items are a bit fuzzy... You will not find very reliable RAW on magic items, only vague exemple you can refer to to help you...
Creating a magic item is more an art than a mechanic... That's why every non "by the book" magic item is not reliable in PFS or if you change GM regularly... 'cause you have to discuss the item with your GM every time you change table... :p
So I can tell you what I would do as a GM for corner case like this but cannot pinpoint you the RAW... :/
Let me give an example as to what I'm looking for:
I have a club; its a +2 club.
I cast wood shape and turn it into a sphere.
Does that mean now I have a +2 sphere (Improvised as a shotput or something as close)?
Nope. Wood Shape is described as only capable of crude items, so the result is likely not masterwork. It may retain a magic aura and might again be a +2 club if returned to its original shape. Ask your GM. Fortunately for your example, Wood Shape is transmutation and not Polymorph Any Object, because PAO can't affect magic items.
Another example is a have a staff (custom made, doesn't matter, its a magical staff).
I cast wood shape and turn it into a sphere.
Does that mean I now have a wooden bauble that functions as a staff?
Perhaps, but you'd still have to handle it like a staff. A generous GM might let you hold it in one or both hands (depending on how your character can use a staff) and still use it.
I have a wooden ring with a constant or at use or command word magical effect. I cast wood shape and turn it into a slotless wooden marble. Would the magic placed stay on the item?
You can't cheat the item creation rules. You now have an item that needs to be equipped in a ring slot to function, but it is a shape that cannot be so equipped. A generous GM might let it function if you have no ring on that hand and hold it in your hand in approximately the right place.
Another example; I have wooden bracers of +2 skill to whatever. I cast wood shape and turn it into a facemask. Does it stay magical?
You now have an item in the wrong slot. It will probably still be magical, but won't function because it's in the wrong slot.
In addition, if the magic is lost for one reason or another, would it regain its magical properties if repaired - I.E. Returning the object to its original state for its intended magical qualities?
Depends on how the repair is made.
If you used Mending, it saysMagic items can be repaired by this spell, but you must have a caster level equal to or higher than that of the object. Magic items that are destroyed (at 0 hit points or less) can be repaired with this spell, but this spell does not restore their magic abilities.
If you used Make Whole, it says
Make whole can fix destroyed magic items (at 0 hit points or less), and restores the magic properties of the item if your caster level is at least twice that of the item.
This is actually a very interesting and inventive way of using transmutation! We always hear stories of a player confounding a DM with their clever ideas and this is a perfect example.
There is some text about altering existing magic items (Ultimate Campaign, pg. 172), mostly to do with creation feats. Then it offers some warnings if you wanted to change those properties.
But the short answer is there might not be explicit RAW for this.
To use wood shape on a magical item - the item would get a save - every time. Magic items always make a save against spells even if unattended.
Outside of that if the item fails the save it's no longer magical - an item has to be masterwork to be magical - and wood shape can only do crude shapes at best.
I'd say make whole would (could?) fix the item back to what it was - the item should also show it's original form? This last part I'm unsure of - expect table variation.
If I have a magical +2 sword, and an enemy casts dispel magic on it, is it now a mundane sword, or is it still a magical sword that happens to have its abilities suppressed?
The distinction becomes important for things like mage hand, or shatter, which can only effect non-magical items, or for other effects that restrict saving throws tow magical items, but not mundane items.