Did just the axle bolt break off in the shaft? From the pictures, it looks to me like you might be able to get the stub of the broken axel bolt out of the shaft. You might have to use a set of reverse drill bits and bolt removers. then get a new axel bolt and you're set to go.
It's a little hard to tell, but it looks like either the axel bolt broke off, or the threads on it are stripped. If they are strpped, you might be able to clean out the threads in the shaft, get a new axel bolt, and you're back in business. Take a look at the parts break down on this web site and see how things go together. I'm familiar with the HR214, and I believe the transmission and all is the same as the HRA214. The wheels are held onto the shaft by a bolt, and it just looks like someone over tightened it and stripped the threads from your pictures.
$20 is a great deal on the engine alone. From the little bit of the deck I can see, it looks like it's in good shape. Take some time and look over all of the parts diagrams and sort of familiarize yourself with them and see if it looks complete. I know there's quite a bit of information here about the HR214 with the aluminum deck, but not a lot about the HRA214 with the steel deck, so what you learn about yours and share here will be great to have.