We are having really hard time making a good background music for our game. Can we use some free musics in our game?

I don't think you can according to the rules. Brackeys has done a video on using Bosca Ceoil but I'm sitting in the same boat that I don't know what music to make. I'm trying follow this guide which seems promising.

My solution requires an iPad:

I’m lucky enough to have musician friends and so I could partner up with one of them. To show him what I had in mind in sort of tone and feel to the music I decided to make a temp track, facing with the same problems I remembered that I own an iPad and Apple has published this amazing(!) piece of Software called "Garage band" where you can smartedit your own songs. I have to confess that I do know something about music, but it’s not really much.

tl/dr: If you do have an iPad give GarageBand a try.

And if you don't have an iPad, I just found this nifty website, www.soundtrap.com, that acts similar to it.