How to say: no problem in Chinese Mandarin.
Like a reply to thank you. is it 没关系? or do you use something else?

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Answer

depends, if you want to reply thank you, you might say 不客氣；if you want to reply sorry, you can use 沒關係；but if you want to express you will do something that someone told you to do, then you better say 沒問題～。

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normally,wu use"不客气or不用谢"to reply people ,but to people who is familiar to us,we say"嗯，好的","没关系"is used when sb say"sorry"to you

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when it replys  THANK YOU, you can understand it as 没关系.the person just wants to express the emotion for welcome.U can also say 不客气，没事，好的。

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没问题。
好的，没问题。
包在我身上。
行。
好的。
行/好的，知道了。