P0446 after Right-Rear Collision & Refuel - Gen 2 Prius (2004) - Rough Idle/Start Body:

But damages are on side opposing the filler tube and related tubing . Isn't cannister for evap kinda centered under car above tank ,??? Unless rear quarter is pushed do far as to crumple spare tire well? And push that area to canister a quick look under car would tell srory. Or pics from under car?

 

Be careful not to jump to conclusions. It may be related, or not.

 

You need to vacuum test the system for leaks and isolate the it from the back or front of the car.
Your in a hot humid climate, so for a car that old, those rubber seals on the valves will corrode and fall apart. There's also the distinct possibility that you got some contaminated fuel. I know they sell fuel on every corner, out of a liter or two soda containers - at least they used to do that a decade ago. I would start with the gas cap seal. That's the most common issue.
Your rear wheel may be out of alignment or your traction battery pack is going bad. When was the last time you cleaned out your traction battery cooling assembly? You should check the traction pack with the Dr Prius app.

Good Luck....

 

Second on checking the gas cap seal. A loose or leaking cap is the most common source of that code (on most cars, anyway).

Running rough could be a vacuum leak, probably up front. Or it could be any of the other usual suspects, like fuel problems, bad plugs, dirty injectors, an iffy coil pack, and so on. It may or may not have anything to do with the accident. The rough transitions are probably from the plate between the motor and the transmission trying to compensate for the motor running poorly. Whenever the ICE is not happy that plate will let you know. This video gives an overview of what I'm talking about: