I'm not sure if you've explored Heath Check which is still in preview, but I would look at that. You can create an alert that will trigger should the health check count not meet expectations.
- As you are already aware, WMIC can't be accessed from the sanbox. One workaround you could do would be to host your app in a docker container. If you got that, make sure you use one of the cached images to avoid container start time timeouts.
- I'm not aware of any 3rd party agents off hand, but you can easily create a service application that pings your app service and reports however you want/need it to. I will say though that Azure Monitor is quite comprehensive should you want to review 1st party service.