Q: can I downloud apple softwere on my surface rt?

I'd check with Microsoft.

iTunes doesn't run on Windows RT, and it seems highly unlikely that it ever will (no motivation for Apple to port to a platform that's a direct rival to iPad and has insufficient market presence to impact on usage of other iDevices).  Obviously the Surface Pro models, which run full Windows 8, is fully compatible with iTunes.  Given that MS have launched a third generation Surface Pro but not a corresponding RT device one could wonder whether the latter platform has much of a future.