"Unable to access java file" means you typed in the path wrong- the part you were supposed to replace "full/path/to/game" with. The path to the file will probably lead to somewhere in your downloads folder. What did you type instead there?
I've never heard of a crash during play- crashes during loading as you described are common, but unless you're using the Koopalings, nothing loads while matches are playing. The memory used should stay constant throughout a match.
If the game crashes, the music will continue to play until the error goes away and the game closes. If it's still playing after the game is closed, something is very wrong. Are you sure you actually closed out that first SSBS.jar file?
What are the java error codes? Sure, you don't understand them, but I might, and I can't troubleshoot if you don't tell me everything.
Are you saying that the game crashes when you go into the options menu? I can't think of any reason why that would happen, unless you deleted the font files or your save file. The most likely explanation is that having two copies of the game open made one version of the game modify the save file while the other version was using it... but still, that's pretty weird.