According to the rules:
Each field is worth 3 points per adjacent completed city.
So the city must share a line with the field. It does this for three of the cities. The small vertical city is adjacent to two fields which does not connect to the field with the red meeple, so this one does not count.
The official, pre-expansion rule to keep track of 50 points was to lay down the scoring meeple like a farmer.
Start of page 4 of the official rules (pdf):
Note: if your score passes 50 points, lay down your scoring meeple to show your 50+ points
Of course, any way to mark 50+ or 100+ points that your group agrees on and that can be clearly distinguished ...
frodoskywalker's answer is correct but not comprehensive. Here are other aspects to consider.
The rules for Hills & Sheep say, "When a player places a tile featuring a field, she may decide to place a shepherd on that field instead of placing a follower..." So you can not ever place a shepherd AND a follower on the same turn. Often, you would be able ...
When you reveal a dragon tile, you place the tile, then place a meeple (or move the fairy), then the dragon moves.
Moving the fairy replaces a meeple placement, and you may place a meeple before the dragon moves. From the German rules
Der Drache (12 Karten)
Sobald eine Karte mit einem Drachen aufgedeckt wird, legt der Spieler sie wie gewohnt an und darf ...