Hi Irina,
Your first sentence is grammatically sound.
As for your second sentence, we don't say or write: "... pleased to know your news."
The word "news" refer to a piece of information about recent events as reported by means of newspapers or web sites. When your friend updates you on what has happened in his or her life recently, it is not a piece of news.
Perhaps you can write: "I am pleased to catch up with you."
Hope this helps.
Cheers, Lance