I was reviewing your interesting questions and my answer to them differ from the one provided above (
@NGC 54, please check my comments below).
-Picture 1: can the tile bottom left be placed? The only tile next to it is a half tile, and this position would place it next to the empty half space.
We considered that this is allowed, since the space next to it is considered occupied by a tile, but we weren't sure.
In this case, the placement should not be allowed.
Revisiting the Halflings rules, you may read:
The half-sized tiles are placed according to the rules of the Carcassonne base game, meaning that at least one side of your tile has to continue the landscape of one or more existing tiles.
When placing a tile next to a Halfling, the reciprocal rule should be applied: a tile may only be placed next to a short side of a Halfling tile, never next to a triangular space (if not next to any other tile edge). The later would be similar to a corner-to-corner invalid placement.
-Picture 2: pink places the half tile to complete her city. Does it limit the Mist?
We considered it didn't.
In this case, the triangular gap should not be considered as limiting the mist, since the placement of a second Halfling tile filling the triangular gap would limit the mist at the same edge for a second time. This would be awkward, so only and edge-to-edge placement may limit or extend the mist.
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