Why is there metal cases on some of the vacuum tubes and are they actually needed?
The metal cases are to provide RF shielding for the tubes--& yes,if they were fitted originally,they are
needed.
I've heard this radio can do three ranges, police, shortwave, and "Broadcast". Does that mean AM?
Back in the day,the Police operated on Shortwave (HF),so that is why it is marked on the dial.
"Shortwave" (HF) is nominally between around 3MHz or so to 30 MHz.
You will probably find that this radio will tune up to maybe,12MHz.
It is an AM radio,so it will receive AM stations on the Medium Wave Broadcast Band,& Short Wave AM broadcasts on the "Shortwave" bands.
Hams,& other Communications users on HF,usually do not use Amplitude Modulation,although if you are very lucky,you might find some.
What are those large rectangular cans protruding upward from the chassis. One has a wire connecting to the top of a tube. Are these capacitors?
They are Intermediate Frequency (IF) transformers,which are tuned to the IF frequency,which is usually around 455kHz,although some old radios use 175KHz,or 221kHz.
The wire to the top of a tube is probably so the secondary of the transformer can be connected to the Control grid of the tube it is connected to----some tubes,but not all,had this configuration.
Theres four wires going to a single speaker?
Back in the day,Electrodynamic Speakers were common,as Permanent Magnets were not developed to the level they were in later years.
The HT line from the power supply was run through the magnet coil,doing two jobs--acting as a smoothing inductor for the power supply,& an electromagnet for the speaker.