Will we be graded on the compositions of the background music? I am not a composer, I am just asking because this could be a bit unfair if someone uses say, classical music, as background music and it is a more complete composition than another contestant's original track.

Your game will be rated by other participants - as per the rules, people are allowed to use whatever assets they have the rights to.

Everyone has to explicitly declare which assets were made before the jam in the description. Most people will take that into consideration when giving their ratings! 

Also, the rating guidance says, for audio:

- How good does the game sound? This isn’t necessarily about technical skill here, do the music and sound effects fit the gameplay?

Games that just throw in a classical piece will likely be rated lower, because they don't usually fit the gameplay. Things like that don't usually loop very well, and it takes a LOT of time and effort to find free or paid asset packs that have a cohesive theme.

Also worth noting:

This is a friendly jam - not a competition

Yes, there's a small prize - but there are likely to be 200+ entries, and skill will only usually get you into the top 10%. Winning a jam is strongly luck-based, e.g. if your game is amazing but gets played by someone after a game that was made by a team of 5 industry professionals who have been making games for the last 30 years, that person is probably going to rate your game lower than if they, for example, played it after someone's first game that barely runs. Your game might also be rated by someone who just doesn't "get" the concept, or hates the genre of game you've made, or is playing on a crap laptop and has a ton of performance issues. There's too much that is out of your control for events like this to be a serious competition!