Yes, yes to all of these things.
1) You can write the batch file so it can be double-clicked.
2) You can put your classes in a "jar" file, with a proper manifest, and configure your desktop to run the file when double-clicked.
3) There
are tools that make .exe files out of Java code, but they're frowned on; the "executable jar file" approach in #2 is portable to all OSs, and so is the preferred technique.
Here is one of many documents explaining how to do #2.