You have the API for Windows Phone don't you. It supports background downloads, even I can switch apps, then lock screen and they go on. DON'T EVER REMOVE THIS. And please if possible tell if that's really not that difficult or you have some exclusive stuff from Microsoft.
But sadly downloads don't get saved to an SD card or a phone memory(maybe in the app data), and that permissions are unrestricted now in windows phone. Exactly like your java version you can, so you can show where files are from your window as well as from windows phone's interface. Saved pages should get saved somewhere accessible and associated to Opera for Secondary memories too
Let's admit one thing, you are not real quick in coming here. I can understand it's beta and without feedback you can't improve performance issues. But if you think you can do this slowly then there are other browser who will go faster than you. For now it's fast, and can open numerous tabs(with background support). But if people didn't care you will be left far behind and they won't be able to get the best of what only you can do.
*you should get opera keyboard as an extra option.
*Always let it load pages like this or get another Opera Mini and make this Opera Mini Classic(latter will be better). This is necessary for 2G users and slow internet.
*Sooner(not the late coming soooooon thing) you should get Opera Next(a webkit one), Opera Mobile, Classic and another one designed for Windows Phone(only this should be a non emulated one, would be great if it has multiple modes or could make opera for windows and windows phone same, can run all plug-ins etc. the desktop version can, even the desktop version of adobe flash). It wouldn't be easy but at windows phone you won't be suffering from a shortage of user base. So earlier you gain their attention or worse they get disappointed more early.
*Please add a much much awaited way to remove temporary files or a reset system in side app. In Symbian it crashed a lot due to that. Nowadays we have more RAM but device like 520,530 and other upcoming ones may need that. We too to save space.
I am avoiding to add searches to my browser and speed dials though that's my favorite feature. I think that's causing crashes. Do check that.
I will post more as I explore