yes.
yes, depending on what you use the pc for.
for example, playing a game at 2560x over 1920x can drop your framerate by about half. using a 2560x monitor will require you to spend more on a gpu and update the gpu more frequently if you want to keep the same quality settings and fps.
also keep in mind that movies are 1920x1080 so if you plan on watching movies this is the resolution you want. on 2560x you might see a loss of quality. this applies to other pre rendered material as well. for games and other applications which render on the spot 2560x will be about the same visual quality as 1080p viewed at the same distance. what you gain is not sharpness but overall size since the actual pixels per inch are actually a bit lower.