Do I need to worry if my hot water system drips water constantly?

Is a slow-draining sink or shower something to be concerned about?

Whenever I operate the taps, there is a loud clunking sound. Is this a plumbing problem?

Can I fix my dripping tap? 

Sometimes my toilet cistern needs the flush button pressed many times to stop it leaking into the bowl.

Yes- wasted energy in electricity or gas. If leaking from the case of the unit itself it generally means the cylinder inside has ruptured (new unit reqd.). If leaking out of a valve this means that the valve may need replacing.

Yes it's only mattter of time before it blocks completely. If the pipes are old galvanised pipes it is generally more economical to replace the pipe with a pvc waste pipe. 

Yes. It is generally able to be rectified.

By all means, but the cause of a dripping tap is generally about 85% of the time due to the seat needing to be re-machined which requires a tool that most people do not have. Very rarely is it just the tap washer that needs replacing.

Sometimes the ball float may just need adjusting. Every toilet cistern has an inlet valve and a outlet valve. Both have washers and rubbers in them that do need replacing. I generally show regular customers how to replace them and leave a few washers for them to use if they show some interest in doing the job themselves.