Do the effects of the Shield Wall perk only apply when you're using a shield, or do they also work while blocking with one-hand and two-hand weapons?

And, are the rumours about the Shield spell working like a normal shield true? If so, are they also affected by the Shield Wall perk?

We can't say for certain. My guess would be shield only for the first question; I hope so but doubt it for the second; and if the second is true, I would expect the third to be as well.

Shield wall despite the name states that it increases the effectiveness of *blocking*, which to me suggests it means all blocking, whether using a shield or staff.

As for the "shield", shield... first I've heard.

Alteration shields just boost armor like previous games; there's no blocking done with them. As for the Restoration wards, your guess is as good as mine.

I think Shield Wall affects blocking with weapons as well but I can guarantee you that, no, it will not boost the effectiveness of any magic spells.