You don't need to have flash player installed but you do need the exe file for it. I don't think its possible to have an swf file in an exe file. You could create a batch file to launch flash and load your flash file and convert that into an executable, but it would be 3 files: swf, exe, and another exe.
Theoretically yes you can play flash without flash-player but it would very much pointless because you would need to build an executable that could understand flash files almost 100%. In doing so you basically just rebuilt flash.
Flash Professional (adobe's flash application builder) does make executables that are a flash-player sub along with the real flash file. One file that's an *.exe (the player part/sub) and then the .swf or .flv at the end of the executable sub in the same file.
I don't know, but to what programmer47 said: No, that is false. You can have a SWF file within an exe no problem, after all executable data is just data like any other. Though of course you'd have to put the SWF into a part of the exe that won't be executed. The rest of the exe would be a flash player of some sorts that gets the offset to the SWF content in your exe.