Is there an equivalent to these AWS services in Azure?
These are kind of "rough" pointers since even though the services are basically comparisons to the ones available in AWS, some differences still exist.
For AWS Config, I would recommend Azure Policy https://docs.microsoft.com/azure/azure-policy/azure-policy-introduction
"Azure Policy is a service in Azure that you use to create, assign and, manage policy definitions. Policy definitions enforce different rules and effects over your resources, so those resources stay compliant with your corporate standards and service level agreements. Azure Policy runs an evaluation of your resources, scanning for those not compliant with the policy definitions you have."
For CloudTrail, Log Analytics is pretty similar (sort of) https://docs.microsoft.com/azure/log-analytics/
"Log Analytics is part of Microsoft Azure's overall monitoring solution. Log Analytics monitors cloud and on-premises environments to maintain availability and performance. Get insight across workloads and systems to maintain availability and performance. Learn how to collect, analyze, and act on data with our quickstarts, tutorials and samples."
Basically with Log Analytics, you aggregate logs to your Log Analytics workspace, and onboard several available solutions which provide you insight on your resources, based on the logs that are being ingested. If you are more interested in the management plane alerts (like which user is doing what on your Azure subscriptions), I recommend getting familiar with Azure Activity Log and Azure Monitor:
https://docs.microsoft.com/azure/monitoring-and-diagnostics/monitor-quick-audit-notify-action-in-subscription
For CloudWatch Events, see above and take a look at these
https://docs.microsoft.com/azure/monitoring-and-diagnostics/monitoring-get-started https://docs.microsoft.com/azure/log-analytics/log-analytics-activity
Basically, Activity Log is the service that gathers all actions happening inside an Azure subscription, whether human generated or not.
Hope these help.