Conduktor can connect to multiple ksqlDB clusters at once. It's often useful because it's not always a good idea to have only one large ksqlDB cluster for an environment.
We try our best to be compatible since ksqlDB 0.10.x onwards (up to 0.14 as of today). ksqlDB still being in development, it's possible the developers break stuff to move forward, therefore we need to fix stuff.
If you're using Confluent Cloud, consider reading the dedicated documentation to be sure you're using the right credentials.
The default configuration when starting ksqlDB locally is to connect to http://localhost:8088, as seen below:
Conduktor supports custom headers, basic auth (username/password), and TLS security (1-way or mutual TLS).