I'm pretty sure you're running java- 32 bit. Most computers run on a 64-bit.
Ensure that you're PC is running 64-bit by viewing your system properties. If so, go to java's website and download the 64-bit version. This should help, I hope.
If this doesn't work, then it might be either the launcher you're using, or your computer is limiting your RAM usage by default so it can have room to open other processes.
It's probably crashing because it's refusing to launch the version of forge you're using. Try looking for a different version, maybe an up to date one?
I was looking, but most mods seem to be outdated. The most efficient way is just by running a local server and whitelisting yourself so you'll be the only one accessing it.
If you're looking to make your own server, you are your own experience. You will be the owner, and anyone under obeys to the rules you set out for them.
What you should avoid is plugins that are not verified by bukkit themselves. Some of these plugins that scammers would send you are named something that you would identify as legitimate but will end up be an exploit to your server.
java.lang.ArrayIndexOutOfBoundsException: 0 at org.lwjgl.opengl.LinuxDisplay.getAvailableDisplayModes(LinuxDisplay.java:951) at org.lwjgl.opengl.LinuxDisplay.init(LinuxDisplay.java:738) at org.lwjgl.opengl.Display.<clinit>(Display.java:138)
Right here shows you have a Display issue. Usually caused by launching the game in a certain window, like fullscreen. Try launching the game in a smaller window? If you can't try running an older version of minecraft and change the displays there, then go back.
If this doesn't work, are you running it with optifine? That might also be a problem.