Removing the cloud with the arrow next to all my music?

That symbol is the download-from-iCloud symbol. You cannot remove it as it is there to give you access to the iCloud source.

So, to expand on Ralph's answer, when you are somewhere where you have access to Wifi, download the songs you want on your device by clicking on the cloud so you can listen to them offline. Or, sync what you want on your device via iTunes on the computer your sync with.

Cheers,

GB