Using the internal index, is there a way for me to find out errors being thrown from the different splunk components?
You are probably most interested in the introspection logs. You can read about them in the Troubleshooting Manual, which also includes some sample platform instrumentation searches.
If you have not already done so, you should also look at the Distributed Management Console and the searches that power its dashboards.
I don't know what you mean by components but this is a good search to get you started:
components
index=_internal log_level!=INFO| cluster showcount=t | table cluster_count _raw | sort -cluster_count
