Questions & Answers about Ты хочешь чай или кофе?
Why isn't there a word for "Do" at the beginning of this question?
In Russian, you don't need helping verbs like "do" or "does" to make a question. You use the exact same words as a regular statement (Ты хочешь чай или кофе) and just raise your pitch to show it is a question.
Why do чай and кофе look exactly like their dictionary forms? Shouldn't they change since they are the objects we want?
They actually are in the accusative case! For inanimate masculine nouns like чай, the accusative form is exactly the same as the dictionary form. Кофе is a special borrowed word that never changes its ending at all, no matter its role in the sentence.
Why does the verb хочешь end in -ешь?
This is the present tense ending for ты (informal "you"). The dictionary form is хотеть (to want). It is a slightly irregular verb, but it still follows the common pattern of ending in -ешь when matching with ты.
How would this sentence change if I were speaking to a stranger or a group of people?
You would need to use the formal or plural "you", which is вы. The verb form must match it, so the sentence becomes Вы хотите чай или кофе?