Keeping your PC on can be harmful because the components can get hot. So yes, when you are done using your computer shut it down completely. As for the energy savings, you will see a difference.
Hope this helps,
How much power it saves is dependent on the specs but just turn it off or sleep. Sleep takes usually 5 watts so doesn't really affect your power bill. Calculating 10 hours each night for 30 days is only 1.5 kwh so $0.15 per month if your rate is $0.10 per kwh. Hibernate is like turning it off, it doesn't need power.
You typical don't have to worry about a pc's life. They will usually last much longer than their usable period. The only thing that will always die is the hdd which is usually 5 years and is easily replaced. Keeping it on vs turning it off every night doesn't really make a difference in lifespan.
Keeping your PC on can be harmful because the components can get hot.
A pc at 100% power should not be overheating let alone idling so getting hot is not really relevant. Hotter temps is worse but heating and cooling is also damaging.
Leaving the machine on for extended periods of time (talking months) can lead to decreased performance, because (Citation needed, not sure on this) the OS' temporary files get bogged down over that amount of time.
Unless your computer has the worst cooling imaginable and is chocked with dust, the computer wont overheat at idle. And if its overheating at idle, whenever you use the machine it would probably shut down to protect itself.