The Cabot captain did what she could under the circumstances. In other episodes, they are shown to overwhelm an area quickly and in that was when they were not enhanced. I am not sure if the ability to self-destroy the ship was even possible after the tribbles had invaded the ship's circuitry.
Nightmare fuel - I read the find print with the commercial, where it said that the tribbles could survive being eaten and could multiply in the digestive tract. The thought of those creatures multiplying quickly in the body, causing it to bloat and explode is terrifying to imagine.
If spectrum refers to the autistic spectrum, I can tell you as someone who is autistic - Nope. He is not autistic. He has other mental issues.
Memory Alpha has it stated that the ship exploded, with the tribbles somehow surviving in space and invading the planet nearby, named Pragrine 63, after surviving re-entry. Nope. I believe two scenarios more likely - either another ship came to investigate the wreck, being infected in the process, - we hear of the Cabot rendezvousing with a transport, or the Cabot itself falling from orbit and crashing into the planet. Tribbles might be the equivalent of rats, who hitched a ride on ships.