If the timing belt drives the water pump, then yes, you should replace the pump at the same time as the belt.
A critical maintence item is replacing the cam belt which should have been done at 110,000 miles. If that has not been done then do it immediately. If that belt breaks you will have serious internal engine damage. The water pump & thermostat should be replaced at the same time. If you have not replaced the spark plugs do so now. Inspect the struts, & brakes.
If it is a V6 at 110,000 miles the cam belt and water pump should have been changed. This is an interference engine. If the belt breaks serious engine damage will occur. If you have not had the belt replaced STOP driving the car until you can get this done. The belt can break at any moment. On a V6 & 4 cylinder, you also need to have the transmission fluid, brake fluid, and power steering fluid changed. The coolant needs replacing and thermostat needs replacing. Spark plugs and plug wires need replacing. Air & cabin filter need replacing every 30,000 miles. All suspension and steering parts need inspected and replaced as necessary. More than likely the struts need replacing. The exhaust system should be inspected. Of course the brake system should be inspected and repaired if necessary.
It has a cam belt. This engine is an interference engine and as such if the belt breaks serious engine damage will occur. Do not neglect replacing the belts. This engine has 2 belts that must be replaced at 105,000 miles. Camshaft & Balance Shaft belts. The water pump is also driven by the cam belt and should be replaced at the same time as the belts, as this will save you labor costs later on considering the pump will need replacing before the belts need replacing at 210,000 miles.
This can be a complicated procedure and varies depending on the engine variant. Is it a 5 or 6 cylinder? Does it have intake or exhaust valve timing or both? The timing belt tensioner pulley should also be replaced when replacing the timing belt. The 6 cylinder engine should also have the termostat replaced as well when replacing the timing belt. I may be able to provide detailed instructions if I knew the engine size and year of the vehicle. Also turbo or non turbo.
There is no maintenance schedule for replacing a timing chain. Timing chains are designed to last the life of the engine and are normally replaced during a complete engine rebuild.
If an engine light is still on after replacing a fan's radiator sensor in a RFW engine the coolant sensor should also be checked. If the coolant sensor is bad it will send an error code to the car's computer.
There's no point in replacing the piston rings. You have to completely remove and disassemble the engine in order to reach the rings. In light of the fact that you didn't know this, you should have the ENGINE replaced by a qualified technician.
If this is a DOHC 2.0 it is an Interference engine and you may have serious engine damage. If it is a SOHC 2.0, then you are OK as it is a non-interference engine. If you have replaced the belt, you need to check for engine damage. The belt should have been replaced at 120,000 miles. I suggest a professional look at this, especially if it is the DOHC, as replacing the belt incorrectly will do more damage.
Normally it will last the life of the engine and is replaced when the engine is overhauled.
Never, it is designed to last the life of the engine and is normally replaced when the engine is overhauled.
It is an interference engine. Belt should be replaced approx every 100,000 miles.
No, not if it was done correctly and the engine has not overheated. Overheating is the main cause of a blown head gasket.