Is it possible to call a process model start point from outside of Appian? I wo

You can publish Process Models as web services: forum.appian.com/.../Publishing_Process_Models_as_Web_Services.html
start form inputs become params for the web service

Sure thing! A good way to do that is to use the 'Receive Message' Event Trigger on the Start Node of the process. You can even have an email message start the process. Details are here: forum.appian.com/.../Start_Event_-_Receive_Message.html

We have a few processes that are started by webservice calls and another one that receives a JMS message using the 'receive message' event trigger. Both generally seem to work well. The JMS works flawlessly I think, but the webservice call might be an issue if the calling process is expecting a result/response quickly. One of our developers is attempting to create a tempo user task/form and pass back the task id to the calling webservice (so that a URL link directly to the form can be presented). She is having some issues with timing, i.e. it needs to be quick or the calling webservice may time out.

Ryan - you could also have the process that is started call a defferent webservice provided by the system that originally calls appian's webservice, in effect creating an asynchronous request/response...?

Ryan - Could you please help me understand, how we can have a custom variable/parameter in response when we make a processmodel as a web service?

Web service only returns process instance id.
philb's idea is a good one, though. You'd implement a call back pattern in your calling application.