I believe you need to apply a transformation to your data in ArcMap. Display the Data Frame properties, Coordinate System tab. Set a transformation. ArcMap does appear to have the necessary transformation, see attached image. Once you have your data displaying correctly in ArcMap in wgs84, then you could export a shapefile that will display in ArcGIS Online.
As far as your other question, if you want to display more than 1000 features, then you'll need to purchase a subscription to ArcGIS Online when it becomes available later this year. With a subscription, you can create services hosted by ArcGIS Online.
Hope this helps,
Thanks,
Mike