I use masking to achieve this.
Import your image, then, draw a box or any shape on top of the image.
Then with both selected go to Object--Clipping Mask--Make.
It is advantageous to group the image and its clipping mask.
If you want to isolate a person from an image, use the pen tool to clip a box in shape of said person. Once that path is closed, select both the image and the path you just drew, and do the same thing as above. I prefer to clip images in Photoshop then place them into Illustrator, but this is a rough way to get the job done.
To answer your other question, you'll know vector objects by looking at the Links palette when you have an object selected. If nothing is highlighted in the Links palette, you've got vector artwork.
Mark