Welcome to the forum, dr.kleiner.
I have changed your thread title.
Extract from the Posting Guidelines:
'Thread titles should include all or part of the word/phrase being discussed.'
The first sentence is just fine: 'global warming effects' means exactly the same as 'the effects of global warming'.
In the second example I would hyphenate 'media-pushed issue'. It then means the same as your alternative suggestion.
Please tell us where you found the text you quoted. Both statements are highly contentious.