no you can't make it download with the computer off as there wouldn't be any power to the system, no power no programs running, do what i do, log off (not shut down) and switch the screen off.
You do realise that downloading songs for free is illegal and as such you shouldn't really be asking the people here to aid you in your illegal operation.
Limewire has been shutdown pending an investigation, it won't be long before Frostwire goes the same way.
I'd look for an alternative, such as torrents .. though even these are being targeted.
You can let it continue to seed which is basically sharing the file back to the community, you can stop it seeding, either way it doesn't stop you using the file .. but if you intend to move it to another folder better to right click copy and paste, unless of course you stop seeding then you can...