Is it possible to post to the search form from a third party site?  In other words, the keyword field and search submit button would be on a different site, then it would forward the user to the community site with the search results.  So it would need to accept the POST fields.  The problem I'm having is the search form uses some kind of csrfKey (hidden input) to validify that the search came from the site.  Any way around this?

I'm afraid not

May be better using API for that search connection?

Anyway if you need to post to search you can create dirty way for that.

1. Make a forcelogin file (it will give to you authenticated session)
2. Do a search and get an answer
3. Close connection / store it for the other searches

Be careful - you need to restrict access to your force login file by the correct web-server params (like a grant access only from special ip address ranges) and this script shoud auth as some special created standard users with default permissions. You might sure for this user can get only public search results

Simple example of forcelogin script i posted recently here as another question:

 

Thank you for the feedback!   Is there any documentation for using the API for search calls?  I've looked and can't find anything specifically for that.

There is no way, at present, to perform a search through the REST API I'm afraid.