1440p VS 1080p

Generally, no, you do not see more, but it is clearer.

yes and no.

in some games the heads up display (HUD) articles shrink down based on your resolution and in some games they do not. this could potentially increase viewable space in certain games.

as far as seeing left or right? that is controlled by field of view (FOV) and is an in game option. playing on a 1440p monitor with 90FOV will show less than on a 1080p monitor with 100FOV. and vice versa of course. some games allow for higher FOV angles but 90-100 is most common i would say.

as far as clarity is concerned, this depends on the size of the monitors. if you have a 26" 1080p screen then a 30" 1440p screen might look more clear. however if you are using a 20" or 22" 1080p you might not notice the difference as much.

in general though, a 1440p panel gives you more screen real estate, which is usefull for windows.

the downsides are that you require better hardware to max out games at that resolution and 1080p video does not quite look as good as it will on a 1080p native resolution screen.