Ah, the delightful minefield of parsing and when there aren't commas.
And can start a new clause without needing a comma. The verb and subject (and sometimes an adverb or two) can also distribute over an 'and'. In this case, there is certainly distributes over the 'and', making it equivalent to:
While there is certainly room and there is certainly a need for some manufactured plastic in our lives...
This is two statements:
(technically, the adjective "for some manufactured plastic in our lives" could also distribute over the and - it's impossible to tell if that was the author's intent, but if it was, the first statement is "there is certainly room for some manufactured plastic in our lives")
It's not obvious that it should be read that way, except by long practice. It could be made less ambiguous by a comma before the and, but such a comma is not required.
Now, starting from what you got as a quiz, this is hard to explain. I've explained why is isn't wrong, but why is are wrong? Well, the easiest way to explain it is that it sounds wrong because it's followed by a singular noun. In actual usage, natives don't use are because is isn't wrong and are sounds wrong with a singular as an apparent object (unless the subject is plural, of course). That's just one theory, and I don't doubt there are others, but hopefully it works for you.