How can I monitor a process

We have built an application in vb.net 2010 which imports data records to QuickBooks. From our own application, we are invoking a third party
application thru command shell. There are two possible scenarios once we invoke the third party application as below:

Dim p As New System.Diagnostics.Process()
p.StartInfo.FileName = "Name of the executable"
p.StartInfo.Arguments = "paramters list"
p.Start()

1) The third party application launches fine, it goes ahead and produces a log file.
2) The third party application does not launch correctly due to the wrong command line parameters or due to some other reasons
   In this case, the third party application displays a message box with a specific information - we need to grab that error message


We need to know the status of the third party application - if it is processing the records or it has displayed the error message. In both cases,
the process is running, has not exited and is responding. Is there any API call that we can use to determine the state of the process? Can we use the handle of the process to know the state?
Can we use Windows messages to grab the information displayed in the message box?