Can I apply TDR when MB+ network is on? Or I have to shut down the network and the application devices (PLC, etc.)?

 

Using a TDR on a MB+ network will be the very last step. 99% out of all problems can be solved with a multimeter and commonsense.

The MB+ network is typically RS485 so a 120 Resistance at each end. So for an ideal network you should measure 60 Ohms & cable restistance, anywhere above 75 Ohms and it will go wrong typically under 70 Ohms and your fine.
If you have a large network >10 slaves you will be able to measure the resistance on a running network officially you should unplug all slaves before you start your test with the Multimeter.
In 99% of the cases cable resistance is the issue, look at the tabs or remount all connections in case of doubt.

Good Luck ROD