Question

What is the purpose of having fuses or circuit breakers in electric circuits? How should they be connected in circuits so they will be effective?

Answer 1

The purpose of the fuse is to protect the equipment receiving power from overload or short circuit. Having no fuse could result in destroying the equipment and/or a fire.
In buildings the fuse protection (or circuit breakers) also protects the building wiring.
While it is true enough that fuses are used to protect connected equipment and respond to direct faults, the size or rating of the fuse is determined, with limited exceptions, to protect the wiring system from damage caused by overheating due to imposition of currents higher than that for which the conductor insulation is rated.
Your circuit is a chain of devices. This chain is only as strong as its weakest link. The rating in question here is current. When too much current is pulled through the chain, the weakest link gets hot. If this goes on too long, the weakest link may catch fire. If the weakest link is near flammable materials, it may catch them on fire.
Fuses or circuit breakers are designed to be, and must be, the weakest link in the chain. If too much current is drawn, the fuse burns open in a controlled environment as opposed to the wire in the wall. This also alerts the user to the problem, who can correct it and replace the fuse. (Or put a penny in it and watch the firetrucks