If you use coal, it is advised to clean your chimney once a year, to prevent the buildup of coal tar.
If you burn wood in your stove, it is recommended to clean your chimney every 1-2 years.
In both cases, it is best to use a professional chimney sweep to clean your chimney.

Wood-only stoves can only burn wood safely, because the stove gets too hot when burning coal,
Multi-fuel stoves can burn both coal and wood, and have a grill to protect against heat damage, and an ash tray to collect the coal ash.

In most circumstances, the answer is yes, except for modern houses with a Class 1 brick chimney.

Grate: Depending on your usage, the grate will eventually need replacing. Grates slot in easily, so replacing them is easy to do.
Firebricks: Firebricks keep the side of the stove away from the fuel, and will need to be replaced from time to time.
Glass: The glass can crack from rough treatment. They are attached with 4 screws, and are easy to replace yourself.

An Air-Wash system has an air vents, controlled by a lever on the bottom of the stove, which draws clean air over the glass to protect and clean it.