The skin may be a kind of virus, as this has not been documented before. I am sorry of what happened, but the skin must be corrupted. From where did you download the skin?
This is unfortunately common. The way i fix it is by exiting the world (the host of the multiplayer game) and going back in. If this doesn't work, you could both reset your games.
This is an intended freature, the light block can only be destroy with full blocks, and those you mentioned are known as "transparent blocks"
This is like an intended freature, as a player only can stand in a half slab or on a full block, so it won't work like in Java Edition.
This happened to me earlier. Unfortunately, i don't know anyway to fix this, although it's not that big of a deal