In this case, we have to include at least the start-tag. Secondly, it usually helps to include the tags just as a reminder that the elements are there. In the end, it boils down to whether or not you're willing to believe in the existence of something you can't see with your own eyes. But in the end it's really a matter of faith. The answer to the second question should also be obvious if you've been getting into the spirit of things.
Elements are there to help organize the document in a logical fashion.
The HTML element is the all-encompassing element, the HEAD element contains information about the document, and the BODY element contains the document itself. This is a useful distinction and makes things easier to organize. It would be a lot messier if, for instance, you had a load of LINK elements sprinkled around your document. By organizing them and putting them all in the HEAD element, the document makes more sense. This depends entirely on the element.