It affects any kind of drops in the game. the number of drops that you get and what kind they are. so solo farming you get better drops because the chance is just your self rather than spread over the whole group of heros or pugs.
No, doesnt matter if u're 1 or 8 clearing fow, the Chest of Fow still drop you 1 key, 1 shard one gold or another gem, or whatever it is.
Havent done pve in a while, but anyway, other peoples doesnt affect the drops from the chest at the end.
It's like a chest u open with a key.