Should I build my own parts for making PCB with eagle or is there a database somewhere?
Parts are difficult to make standard; depending on technology used to make a PCB certain features must be resized while certain other features must stay the same. Also, the  libraries included with the editor are often too large to be useful - you spend more time looking for a part than what it would take to draw one from scratch. On the other hand, redrawing everything would be silly. Make your own libraries, copy included parts as needed, i.e., only ones you're actually using, and draw the parts which are not included. Sparkfun has nice tutorials on Eagle libraries.