Debugging the app won't help seeing where it connects. It's not how a debugger works.
You have to disassemble the code and see where the link is hardcoded into the app.
To monitor the traffic, you should be familiar with Wireshark and have a rooted android phone. Then you can install "
Shark for root" and log the traffic, then use Wireshark or "Shark reader" for android to analyze the log.
TBH all this is not worth the shit you're doing, specially when you don't know anything about what I just explained.
Also "log in the server" is not a clear description of what do you want, but assuming you mean the logs the creator keeps on the server, you cannot access them without breaking into the server in the first place.
If you want to change something in an online game, only thing to accomplish something is to tamper with the traffic, which AFAIK cannot be done with android alone.