Infinitive with or without to

[Emanuelli]

Thanks for your last help, and talking about infinitive I still have some questions.
1. I ask: "What will you never do"? Which is the correct answer:
a) Study Chinese. b) To study Chinese c) Studying Chinese
Is more than one option right? Why?

2. I've seen in a Grammar Book: "Studying English is good" and "To study English is good". What's the difference?

3. If I say: "Which is better: to live in the city or to live in the countryside"? Is the use of "to" right? Can't I say "living"?

4. For example, someone says: "Tell me three verbs that expresses greetings.
Which is correct: to hug, to kiss, to cuddle (or) hug, kiss, cuddle?

Thanks
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[Casiopea]

1a. What will you never do?
a) Study Chinese b) To study Chinese c) Studying Chinese

1b. What do you never want to do?
a) Study Chinese b) To study Chinese c) Studying Chinese

2a. Studying English is good. ('-ing' means, you've done it before)
2b. To study English is good. ('To' means, you haven't done it yet)

3. Which is better, living in the city or living the countryside?

4. Three verbs: to hug ~ hug, to kiss ~ kiss, to cuddle ~ cuddle