Job/run parameters
When the notebook is run as a job, then any job parameters can be fetched as a dictionary using the dbutils package that Databricks automatically provides and imports. Here's the code:
run_parameters = dbutils.notebook.entry_point.getCurrentBindings()
If the job parameters were {"foo": "bar"}, then the result of the code above gives you the dict {'foo': 'bar'}. Note that Databricks only allows job parameter mappings of str to str, so keys and values will always be strings.
Note that if the notebook is run interactively (not as a job), then the dict will be empty. The getCurrentBinding() method also appears to work for getting any active widget values for the notebook (when run interactively).
Getting the jobId and runId
To get the jobId and runId you can get a context json from dbutils that contains that information. (Adapted from databricks forum):
import json
context_str = dbutils.notebook.entry_point.getDbutils().notebook().getContext().toJson()
context = json.loads(context_str)
run_id_obj = context.get('currentRunId', {})
run_id = run_id_obj.get('id', None) if run_id_obj else None
job_id = context.get('tags', {}).get('jobId', None)
So within the context object, the path of keys for runId is currentRunId > id and the path of keys to jobId is tags > jobId.