I suspect that this will probably be on that will vary a bit from country to country. I can only speak from my experiences in Ireland:

 - No, you are under no obligation to tell your current employer that you're looking for a new job
 - Yes, it would be usual to ask your current employer for a reference (though typically only once you've resigned)

Exceptions to the first rule might include situations where you're a one-person team and you don't want to leave your current employer in the lurch. However, these truly are exceptions, and not the rule. In general, giving your employer an opportunity to replace you is what a notice period is for.