Yeah. For now. Eventually, the 360 will cease to be supported, and when it does, re-downloading anything will be impossible.
Won't happen for a long time yet. The Xbox 360's market place/online systems are being integrated into the Xbox One's at various levels.
Plus there are still millions of 360 gamers, by the time the original Xbox's online was shut off, it's population was almost non-existent.
You can't make true backup copies, though, at least not through the means provided to you by MS (and I imagine the means of making actual backup copies isn't exactly legal).
It most certainly is legal. It is still tied to my license/console. It's on external drives.
Plus I can legally make backups of all my games if I own the original copy anyway, my countries consumer protections tend to be a little better than the US and UK in that regard.
Do bootlegs really count, though? Sure, if you pirate everything, then finding discontinued content digitally ought not be a problem. But the second-hand market for physical is perfectly legal.
2nd hand sales would be illegal if publishers and platform holders got their way. :P