If I say: I'll give you some advice or I'll tell you some news; does it mean that I will give you more than one advice and I'll tell you more than one news. Does it mean the same as two or three pieces of advice and two or three pieces of news?

Hi Newguest.

Cool avatar.

Anyway, both "advice" and "news" are noncount. If I have "some advice" for you, I may have only one thing to say, or several. It's the same with news. If I want to convey that I have a lot of news for you, I may say "I have several bits of news for you" or "several news items to share with you."

It sounds odd for me to hear "several pieces of advice" if they are all coming from the same person - that person is giving advice, period. However, if you say "Jim asked all of the senior managers in the department for input, and he got several good pieces of advice" that makes sense because the advice is coming from many people. I won't say it's wrong to say "I have several pieces of advice for you," but it sounds odd to me.
Once again, Barbara is totally correct. If you want to stress that you have just ONE of those things (advice/news) use 'piece of' or 'bit of'.
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