"copo" is "glass" or "container to put a drink in" and "xicara" is "cup" as in a teacup or the measure of a cup. The problem comes when in English we sometimes call a glass a cup, for example a plastic cup which is larger than 8 oz. is still called a cup. In English, a small cup to drink out of might be made of glass. So "copo" can include certain kinds of "cup" as well as "glass". Another problem is that the metric system is used there and there is such a thing as a "copo Americano" which has a measure of 250ml. http://dictionary.reverso.net/portuguese-english/xicara http://dictionary.reverso.net/portuguese-english/copo
So the English word "cup" could refer to "xicara" or it could refer to "copo", but they are not exactly the same thing. The English word "glass" would translate as "copo". "a tea cup" or "coffee cup" would be "xicara". Now those big coffee mugs or large coffee from Starbucks would be "copo". The encyclopedia indicates that "copo" is cylindrical. I am not sure "xicara" (Brazilian Portuguese) or "chávena" ( used in Portugal) is that shape as it is a bit more open on the top from what I have seen.
The acute accent in "água" is used only to indicate unusual stress. In romance languages the stress is normally on the second-to-last vowel. There are some rules if it should actually fall on the last vowel in Portuguese. If these rules are not followed for a given word, the stress must be marked with an acute accent. I'm not sure if this leads to any other difference in pronunciation.
It might be a joke, but this is an educational program and all through the level of English has very poor. I was not aware of the possibility of reporting. As a school teacher I would say that it is important that it is a glass of water. The jokes can be in their own chapter :)