I agree with you, this doesn't make much sense. The source quote is saying that someone saw a red cover in the water. How would the cover survive going through an engine? It should be shredded. Also, if the cover was left on it would have been sucked into the engine as soon as the pilot turned the engines on or when he when to full power before taking off. Makes more sense if a cover was left unsecured on the flight deck and was sucked in during take off. It still would be shredded though I would think.

Yeah, I can't see it quite happening the way the Sun intimates. Can't rule out FOD ingestion, but highly impropably could it have been an intake covers left on.

Is there a roll on an aircraft carrier?

There is on this one, it's a jump ramp carrier, not a catapult launch.