Hi Kristina,
1. I'd suggest to check the ULS log and Event Viewer for any error that would block the activation.
One thing that they should do is write a power shell script that would go through all the sites and activate Quest Web Parts feature. They don't need to write the activation script for each site but a generic script that would enumerate all sites and activate the feature.
2. When you say "all changes and customizations" you mean the web part configuration and/or custom skins? For the custom skin this is expected since we upgraded our Telerik controls and the old skins have to be updated (this link provides a tool for building new Telerik skins http://stylebuilder.telerik.com/)
If the web part configuration (except skins) wasn't preserved then we need to investigate further the cause.