Near the beginning of the game, you can trigger the fight with Dancer of the Boreal Valley far earlier than intended. Besting her would allow the player to access late game areas from the outset. However, I know of at least a few NPCs' quests are affected by going to certain areas. I especially don't want to upset a certain NPC, as this person's quest could affect the ending.
No. Having done runs where I killed the Dancer at the appropriate time, at the first opportunity and in the middle of Sirris and Yuria's questlines, neither got upset or had any change. As far as I can tell, only specific events can anger NPCs, it shouldn't be any problem if you follow their questline.
The possible consequences are:
You can get the Eyes of a firekeeper sooner, but it doesn't force anything
You can get the Path of the Dragon gesture earlier, it doesn't change anything on it's own...
You gain access to Lothric Castle and Archdragon Peak earlier than intended, which have a lot more upgrade materials, be carefull no to over-enchant and lock yourself with higher-leveled players, it makes summon covenant a bit more of a pain to level...
You can get a dark tome earlier, triggering the dark path of Irina's quest earlier if you choose to. You might lose Eygon's sign for the Dragonslayer Armour.