Do I get a penalty from the IRS for not renewing my corporation -nonprofit

The IRS will penalize a non-profit if it fails to file its annual return (a 990 or 990-PF). However, generally you would not have personal liability for the failure. Of course, the best practice is to formally dissolve and liquidate the entity when its life has ended. You can set up a new tax-exempt entity in the new state but you have to apply for non-profit status for it with the IRS and the state. Yes, it can be for a different purpose.

The IRS would only penalize you for late filing the corporation's 2013 tax return (Form 990). However, as the other attorney pointed out, this penalty is not likely to apply to you individually. Going forward from here, you can continue using the Florida corporation if you want, but you'd have to register it with the State of Nevada in order to operate there. This is kind of redundant, so it's probably best to dissolve the corporation in Florida, file the final tax return, and create a new corporation in Nevada. You'll have to refile for 501(c)(3) status for the new corporation.