What if I need to pause the automation script and play it dynamically. just like a music player.
Running tests from an IDE should give you the possibility to use a debugger. You can set a breakpoint in the IDE. When you run the test in debug mode and hit the point of the breakpoint the test will stop executing the next commands of the code. When the debugger stops executing the code at the breakpoint you should be able to play freely with the browser. In the IDE you can continue the code again when you are done investigating.
So in your analogy the breakpoint is the pause button and the continue button of the IDE is the play button. You can set as many breakpoints as you like. Some IDE's even support pausing the playback of the code at any point in time.
Each programming language and IDE should support the debugging process. How to set it up for your tools is another question. I suggest you ask help from your development team.
Keep in mind Selenium-server has a session time-out of 30 minutes, so you must continue playback within 30 minutes.