There are several brokers that allow shorting of penny stocks..Interactive Brokers being one..with as little as $2K in margin account.
Yes, they do. And for the privilege, you'll pay $2.50 a share in margin and maintenance. Think that's a reasonable risk/reward scenario? I certainly don't.
You'd have to tie up millions to make a few grand. Though IB rarely offers large amounts of shortable OTC stock.