When we install FAST ESP, does it replace SharePoint 2010's search engine feature? If not then how exactly does it work with SP 2010 search engine?
This is something I still want to spend some more time diving deeper into, but you have the ability to configure both FAST and regular SharePoint Search Service Applications on the same farm. You can configure the mapping at the Web Application level, though I'm not sure if you can support both SharePoint Search and FAST Search on the same Web Application.
I have looked at a couple of client scenarios where only certain sets of content would require FAST, so a hybrid approach was proposed at the farm level, but individual Web Applications would use a specific tool.
I have done this - see my blog on how to do it :-