Your teacher is very strict. (1) is more precise, but (3) is also correct and natural.
✅ Let me give you a bit of advice.
✅ He gave me a lot of advice.
✅ Let me give you some advice.
✅ Let me give you a little advice.
✅ Thanks for the advice.
Like you said, (2) and (4) are wrong, because "advice" is uncountable. (不可算名詞)
❌ advices
❌ Let me give you an advice.
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✅ I can try with a little help from my friends (The Beatles)