目前無問題, 如再有問題, 會立刻通知你

答: 目前無問題, 如再有問題, 會立刻通知你. 謝謝.
What you write - "There is no problem at the moment, if any problem later, I will let u know immediately. Thanks."- is correct except for one grammatical mistake*.
You can change the reply to:
There is no problem at the moment. If *there is any problem later, I will let you know immediately. Thanks.

The answer to "Just like to know if there is update from them. Thanks.", however, can be:
There is no update from them at the moment. If there is any later, I will let you know as soon as possible. Thank you.