The air filter looks lik the OEM filter, which is disposable, rather than reusable. So that's why it won't blow clean.
As far as replacing the airbox lid, I suppose if you can fabricate something that really seals it shut to create the original vacuum, it would work. I'm more of the "find a replacement" guy...there's alwasy someone on this BBS who is parting out a bike, or there's eBay.
I don't really understand part of your explanation. You bought this bike from the original owner, who says that he bought it from the dealer new, and the air box cover was already cut? Somebody did something, and I would guess there might have been another owner in the chain.
I can't address how to tell if the carbs have been changed.