Taking break/vacation during graduate studies/PhD
The answer is of course, yes. In fact, you need to take a break to recharge your batteries.

The answers to the other questions will depend on what the rules are regarding holidays (which is country dependent). I think that our guys get six weeks annually (where as other countries only offer one or two weeks). Our guys can take them in one chunk, but this is sometimes problematic if there are deadlines that need to be met, or tutorials, etc.

The way to deal with your advisor is simply to ask him with a concrete proposal. It is better that you have not bought the plane tickets before you ask, because that will be perceived as an attempt at manipulation by your advisor, which will damage the trust relationship.

When my guys ask for a vacation I simply ask whether it clashes with anything. If not, I grant it.

The pros of taking a couple of holidays is that you will have time to recharge your batteries. The cons of not taking a holiday is that you can burn out.