Hi,
Yes, you can cut them on the contacts as seen here:
Klick me
For connection two stripes together, you could solder the contacts together or buy some conectors,like these for example:
Klick me
This is just an example, this one is for normal LED-Stripes, for RGB you need to have one with four contacts. And they come different shapes, there are also comnectors with short cables so that you could place them on the top and on the side of a PC case or there are 90° corner pieces or ven T-pieces.
You have to make sure that you connect them correctly, so if it's an RGB-LED Strip, then needs to be R to R, G to G and B to B of course