I have recently finished a piece of software and want to publish it as an .exe file so users without Java can use it. Do I run into licencing issues when publishing a version that doesn’t require Processing/Java (I have no commercial intentions with this program). It doesn’t access any java-compilers, so it won’t be able to compile java-code by itselt.
Another question: What files are needed for the .exe to work? I’m sure not every file is needed for the program to run. (I use the 64-bit aplication)
Firstly, though programs like “Launch4j” can help you build executables from JARs, running any Java program without a JRE is impossible! …at least as far as I know (…were you actually able to do this? :0? Congrats!).
[THE FOLLOWING, IS NOT PERFECT LEGAL ADVICE. I’m not a lawyer!]
As for licensing, the Processing library is licensed under LGPL (version 2, I guess?), so it might not be a problem. Of course they thought of all of this when making Processing, …right? 0_0
For any libraries you must’ve added on top, make sure to check out their licenses.
I myself have a project or two online that contain the library (and I guess I’ll remove it from there if issues arise!), and the research I did (I remember reading through GNU’s FAQs for an entire day, or so…) seems to tell me, I wasn’t wrong with doing so 
As for the JRE, I guess one could include an OpenJDK one, but it is only good for you to ask the user to install one on their machine, and keep it up-to-date, anway. I don’t see problems with the Oracle one put by Processing in there by default, though. They must’ve thought about licensing properly when they decided to include that!
Lastly, if you feel that I answered parts of your question wrong because I misunderstood something, or you get new questions from reading my reply, feel absolutely free to ask me back! ":D!~