Learn Turkish: Su şimdi soğuk mu? - Is the water cold now?

The yes/no question particle changes based on 4-way vowel harmony. You always look at the last vowel of the word right before it. The last vowel in soğuk is u. According to the rules of 4-way harmony, if a word ends with an o or u sound, the particle becomes mu.

Where is the word for "is" in this sentence?

Turkish doesn't use a separate word for "is" (the "to be" verb) in simple present-tense sentences for "he", "she", or "it". You simply state the subject and the adjective. So, Su soğuk literally means "Water cold", which means "The water is cold."

Can I put şimdi at the very end, like we say "Is the water cold now" in English?

Standard Turkish word order places time words like şimdi early in the sentence, usually right after the subject (su). While you might hear Su soğuk mu şimdi? in very casual, everyday speech, standard Turkish keeps the time word before the adjective.

Does mu always have to go at the very end of the sentence?

Not always! The question particle goes immediately after the specific thing you want to ask about. Here, it is at the end because you are asking about the coldness. If you wanted to ask "Is it the water (and not the coffee) that is cold now?", you would place the particle right after water: Su mu şimdi soğuk?