"No, please do not."
Translation:Nee, alsjeblieft niet.
"alsjeblieft" (if you please) means "please " and "graag" came up in the dictionary as "like " or "love to " http://webtranslation.paralink.com/translator/default.asp In another page of this lesson, someone explained that when someone asks you if you would like some coffee, that you could answer "Ja, graag." which would be short for I would really like some coffee. Maybe like "Yes, I'd like that." in English as opposed to "Ja, alsjeblieft" which would be "Yes, please". Both would be perfectly polite and acceptable in that situation. There are other times where "alsjeblieft" is used but "graag" would not apply. I tried to get the link to that page, but it did not work, only linking to the entire lesson at the beginning of it. Next time I review this lesson, if I come across it, I will copy the name of the person who explained it, for you.
Yes, they are cognates. It actually breaks down like "alstublieft" -> "als 't u b'lieft" -> "als het u belieft"
The English (archaic) word "liefer" is the comparative of "lief", ie. "more lief", which means "nice" or "lovely" or "agreeable", similar to the Dutch word "lief" (which, I will note, nowadays means "dear" or "sweet" when referring to people).
In Dutch, to make a verb transitive you prepend "be-", so you can imagine how "het belieft" corresponds to something meaning "it is agreeable".
So, putting that together, "als het u belieft" means something like "if it is agreeable (to) you", which is similar to the phrase that "please" came from, namely "if it please you".