Spiders ? No idea.

Storage ? Don't put the car on axle stands Dojj, the suspension drops and when placed under load again it'll squeak like buggery. Get a set of shit rims with shagged tyres and let the car sit on those. There's nothing wrong with a cover as long as it lets the car breathe, mine sits under one all the time. Get a quality tailored fitting indoor breathable cotton cover and you'll be fine.