Well, I'm not completely sure about this, but the realtime preview partially depends on your computers specs i think and weither or not you have used any effects, and how many.
Whilst editing your video, you have a monitor window, here you can check out how things look.
I dont know how to properly explain this, but here goes nothing:
the term realtime measn that what you do, you instantly see on screen.
rendered, means that it needs to computed, and made a file before viewing.
What this monitor window does, is it tries to show the preview in realtime.
This usually happens when the imported video matches the same settings are the project in terms of video-size, codecs and then some. (as a 1 on 1 conversion sort of speak).
When you use effects and stuff, this will no longer be the case and thus needs to be rendered.
If the preview cannot be realtime, it gets choppy. rendering the preview may take a little time, but afterwards, its smooth again.
The only thing here is filesize, these previews will be temporarily stored on your HD, so make sure you have enough space.
As for the slicing, this is one of the features I like best in Premiere compared to some other packages.
You have a 'razorblade' button in the toolbar, using this, you can slice at any time, anywhere in your clip when it's placed in the timeline.
you just click on the video-at the desired moment and it is cut, the most easy way to do it
Hope this helps, sorry for the long story