The Giant Dwarf: You don't need a Redberry Pie to persuade Thrugo to sharpen the axe. You can simply ask him directly. (although I had a Redberry Pie with me at that time)
Go down the ladders and search the crate right near the ladder to get to the second floor of the mill. The kitten is randomly placed in one of the crates of the ground floor, not just the one by the ladder.
Hazeel Cult: Second Sewer Valve: This is located south of the Carnillean mansion a bit south of the bridge, turn it to the left. It should be to the right.
ability to pray at the Altar of nature (+2 to prayer points if prayed with full prayer points) One pray will replenish your Prayer +2. You don't need to pray twice.
Ardougne doesn't have a city-wide running water system. There's a sink in Edmond's house. A single bucket is sufficient, as stated in the items needed.