1) I think you need to turn output buffering in php.ini to avoid the "can't start headers, output already started errors". It really is the PHP internal, have thing to do with LSAPI, LSAPI just do what have been told by the PHP engine.
There is nothing to worry about response headers when running PHP from command. You can run LSAPI PHP from command line, should get the same result as the FCGI PHP.
2) Since the output header has been messed up, it would be difficult for the web server to interpret the response correctly. Due to the missing reply headers, part or whole reply body may be treated as response header, it is likely that the web page is broken in the browser.