It's often, but not always, sarcastic. It all depends on the tone of voice. Don't believe anyone who tells you that English is not a tonal language! We obviously don't use tones in the same way that you use them in Chinese, but the tonal pattern used for a phrase such as 'Thanks a lot' will change the meaning entirely. In spoken exchanges, we don't avoid "Thanks a lot". We do use it - both to thank people and to be sarcastic - because the way that we say it will always make it clear whether the response is sincere or not. I think that a falling tone, in combination with positive body language (e.g. a sincere smile) usually means that the thanks is genuine. A rising tone and/or exaggerated stress, combined with negative body language ( e.g. eye-rolling) means that the speaker is being sarcastic. It may be wise to avoid it in written responses, however. If you write "Thanks a lot", it can be interpreted as a rude "Thanks for nothing!". On italki, we are generally fairly culturally aware, so we wouldn't take offence. In other contexts, a native speaker might misunderstand your meaning.

No, it sounds really natural :)

As an American, I say "thanks a lot" quite often to genuinely express gratitude. It's casual, sincere, and friendly. Only occasionally is it used sarcastically, and when it is, it should be obvious from either the tone of voice (lower, unenthusiastic) and/or context (a situation which does not warrant any thanks). When you say "thanks a lot" in a genuine way, make sure your tone of voice is enthusiastic and sincere. If you sound insincere, it might be interpreted to mean the opposite of what you intended. EXAMPLE (genuine): "Happy birthday! Here's a gift from all of us." "Wow, thanks a lot!" EXAMPLE (sarcastic): "I invited your ex-boyfriend to your birthday party." "Wow, thanks a lot."

No they don't avoid it, mostly it is genuine, but it can be used sarcastically with the right tone of voice. It is usually pretty obvious what is meant from the context.