This neatly brings out the point that you are studying to pass an exam, not to gain knowlege that will be useful in later years!
Fire handling is an evolving subject, constantly changing with new technology and techniques; it is quite understandable that a fixed syllabus will fall behind the real world. You don't want to go asking firemen what happens in the real fire, that will just confuse you!
Increasing approach speed in heavy rain is almost never done for real. However, heavy rain in UK is quite a different matter from heavy rain in the tropics - where if you're voluntarily carrying out an approach in heavy rain you deserve all that's coming to you. Burger Thing is quite right that under most circumstances, you will be more concerned about runway performance; there will be sufficient buffer in normal approach speeds to counter the deleterious effects of rain. Of course, if you're in an Airbus, the aeroplane's probably thought of it all already!
After an overweight landing, your first thought should be brake temperatures. Just as after a reject, you need to know whether you are about to suffer a brake fire (bad news - especially in wheels under full fuel tanks!), and whether or not it's safe to clear the runway (overtemped brakes are difficult to control, and may either lock on or fade altogether). You will have, in most modern airliners, brake temperature and tyre pressures displayed in the flight deck. In extremis, even without a fire, you can weld the brakes up (if they're not carbon), blow the fuse plugs in the tyres and end up with 16 flats on your 747. Best you're stopped when this happens!
Scroggs