1. You are almost correct. The economy behind their policies is unreasonable. (Economy is singular).
(Edit, I see you added your additional details as I was editing my answer. It is correct as you put it in your additional details. You can rephrase it that way.)
Data and Media: No. These will take singular verbs in technical writing. (I can give you published examples if you would like.)
Edit: After I wrote this, I started thinking about it more since data is plural for "datum" but the meaning has changed and we usually say "data point" instead of "datum" these days. So there is more to this one than I answered. When I look again, the standard I write to specifies data as singular. However; Wikipedia discusses this and shows that it can be both. Look at the "Usage in English" section here where it discusses both the singluar and plural usage of "data." http://en.wikipedia.org/wiki/Data
Media has a very similar situation. In the standards and style rules that I have to write to these days, it will be used with a singluar verb, but it looks like it can be singular or plural. As an example, consecutive sentences in this Wikipedia article use the plural verb the first time, and the singular verb the second: http://en.wikipedia.org/wiki/Social_media
2. The first one (was) may be spoken sometimes, but "were" is actually gramatically correct.