I'm sorry to tell you this, but this type of repair is often more trouble than it's worth. First, pressed wood furniture is basically tiny wood chips that are mixed with a glue, and then cut to size. Then they are covered with a veneer. When moisture gets through the veneer, it dissolves the glue causing the bubbles. It also breaks down the wood itself. What you are thinking of doing will remove the bubbles, and maybe make it smoother, but if you sand through the veneer, the stain will look very different compared to the surfaces that still have the veneer on them.
There really is no good way to fix furniture of this type and keep it looking good.
As far as your appliances are concerned, you can spray paint them, but you should first use some fine sandpaper, or a 3M abraisive pad to roughen the surface. Also, try to sand as much of the rust off as possible. Then, use a good primer to seal it first, so the rust will not seep through. This will make the new paint stick better. You can buy paint that is specially designed for appliances as well.
I hope this information is helpful to you. Good luck with your upcoming move as well. I'm here for any follow-up questions you may have.