Sounds like 2 very different issues.
If the transformer is buzzing I would check that all the mounting screws are tight. A small normal vibration on loose metal plates could make the sound a lot worse.
The transistor for your magnet should be easy to find in the manual under the solenoids table. If you don't have a manual, download one from IPDB.
There are a lot of tutorials online on how to test for a bad transistor with a multimeter.
It's likely that the magnet is shorted. Think of it like a chain. Magnet is bad, transistor blows and fuse blows. It could also be that the transistor went bad, the magnet locks on and fuse blows. Same result.
I don't know if testing magnets is the same as testing coils? I'm sure there are posts on this topic somewhere