How to fix smashed wires in washing machine

Appliance parts like are generally specific to the manufacturer and possibly model. My usual approach, which has served me well, is:

1. Find the manufacturer's service website.
2. Do a parts search there, based on the model # and part description. Ideally, check the existing part for a label.
3. If that doesn't work, look for a parts diagram of your model. Often these include part IDs expressly for the purpose of ordering replacements.
4. Based on the part number identified in step 2 or 3, search on google and ebay for the part. Usually you can find it from a third-party retailer for significantly less than ordering direct from the manufacturer.

You might also try a local appliance repair parts store -- they may be able to guide you to find the right part if they are familiar with your brand of appliance.

I wouldn't start cutting out chunks of drywall to fix a small area like that.

Take off the wall plate and remove any loose or crumbling drywall. Apply a piece of fiberglass tape over the area, mud, sand and repeat as necessary to get a blended finish. Then prime and paint to match.

The fiberglass tape is nice for repairs like this because you can stick it to the wall and then mud on top of, unlike paper tape which you need to apply on top of mud. I've fixed a bunch of similar defects like this and several years later there are no cracks and they look great.