Yes, you drink the water after you are done rinsing and cleaning your teeth. I have noticed it can dehyrdate you otherwise, also it helps flush things from your system that might have been stirred up but not expelled from the pull.
The saliva helps to pull the toxins out of your blood while you are pulling....it's a good thing. I did two short pulls my first time, about 5 mins the first time and then another 7 min one right after. I am not sure how toxic you are, if you do not regularly detox you might want to start out with shorter pulls and see how you do on them. As for spitting it out and when it depends on the person. If you have a lot of fillings (like I do) you might want to do shorter pulls and then use fresh oil for another one right afterwards. There are times when I am pulling and all the sudden the oil gets very.....toxic tasting in my mouth, in a weird burny way that does not happen too often but when I does I immediately spit it out. Usually it gets thinner with the toxins, and white and foamy. Some mornings my oil does not get very thin or white...I usually notice more in my later pull. Just pay a lot of attention to your body and how you feel and I think you will do fine.
Read Molly's posts and some of the others who have been at it a longish time. This is only my third week, but I highly recommend it.