Low risk
A push button that stays down, sticks halfway or will not flush is almost always the button, its link or the valve under it, not the pan.
A cistern that takes many minutes to refill after a flush has too little water arriving: a part-closed valve, a clogged inlet or a pressure problem.
A flush that barely clears the bowl, with no blockage, usually has too little water behind it or scale in the rim jets.
A hiss, whistle, hum or bang while the cistern refills points at the inlet valve or the pressure behind it, not the flush.
Caution
Water from under or behind the cistern, with the pan base dry, is escaping at the cistern bolts, the supply connector or the flush pipe joint.
Describe the job and get a fixed price from a local plumber.