For example, there's Asphalt which I'd like to play on my Xbox 360 but it's WP8 only, isn't it possible at all to have it on 360 or transfer it? The indie games on the 360 are like browser-quality games, only a small amount I've played actually are great (Apple Jack 2).
Its not possible to simply copy it across, the 360 uses a PPC processor where as Windows Phone devices use ARM processors. The game would need to be re complied for PPC processors, code changed for the 360, controller support added, optimised for the 360's hardware and probably a lot more! Sadly what your asking is basically the same as "will PS3 games play on the 360".
Well actually Windows Phone 7 uses managed code, which is platform independent and games are made with the same tools as Xbox Live Indie games (XNA). Windows Phone 7 games could work on Xbox 360 with minor modifications (over 90% of the code could be shared), but which platforms to support is up to the developer of the game. Of course the game could be decompiled and ported manually, but I don't think anyone is going to do that Easiest way to play is to buy a Windows Phone, I suggest to wait a few months until powerful WP8 devices come out.