Hey Abenezer
When deploying the CData connectors on your sisense deployment the license is included. You will not have to purchase additional connector licenses. Be aware that the connectors cannot be used anywhere else. If you use them locally without a sisense deployment, it will need a license key.
What do you mean with custom connectors? If it is a Cdata connector then you will find some logs in the build-logs, however cdata does have the parameter to store logs somewhere on the server. If you pick the correct path you can view those logs from the Sisense File manager browser (build logs need SSH). If it is a self-build connector then I think you will need to program the logging and let it store somewhere
Hamza