Slicing a large image won't necessarily make it display faster or slower. There are various factors that can make a sliced image faster, and offsetting factors which can make a sliced image slower. Much depends on the individual project, browser, design, and perceptual issues.
Browsers can usually download multiple streams at a time.
That's because the browser has to wait for each package of information to arrive. Because of this, most browsers speed up their overall download by making multiple file requests at the same time. In practice, many browsers are set up to handle four simultaneous streams. It's possible to handle more simultaneous streams, but then packets can start bumping into each other, so four simultaneous downloads is a common setting. When a browser requests a file, there are usually four steps of negotiation.