[Q1] What happens after drawing an unplaceable tile if you want to open a gift?
[A1] You are only allowed to open a gift once you draw a placeable tile.
If you draw an unplaceable tile, you will discard it and draw a new one as many times as necessary until you draw a valid tile. At this point, you will be able to open a gift before placing the valid tile. As a consequence, if the last tile of the game is unplaceable, you will not be allowed to open a gift.