How do you think? How are you? What a lovely phrase. Spoken English, you use this word very well and accurately. Because this does not omit are. The word "are" in the sentence cannot be omitted, just because it is read quickly and weakened to be inaudible.

There is a question mark because it is a question in itself. It means; How are you, handsome? So it's normal to use question marks.

What are you doing? What are you doing? The oral form of. It is also because of weakening. Just like the last one.

The weakening of spoken language is as important as stress. Unfortunately, we don't talk or practice in English class.

What do you think Calgary is like? What do you think of Gregory? What do you think of Gregory?

How to answer is your business. I don't know if you like Gregory. But if you are from Daqing, I suggest you say I like this city. Because Daqing is huge and twin cities.