1. You have not mentioned if the power steering (PS) fluid level has been dropping and you have to keep topping it up. If you are topping it up, and there is no sign of an external PS fluid leak, then there will be an internal leak in the system which will affect PS performance.
2. If you are experiencing heavy steering and hence poor PS assistance in all conditions (ie. assistance does not improve after driving for a while) the most likely cause is either:
a. The PS pump is weak and needs to be replaced because it cannot build up sufficient pressure; or
b. A piston seal inside the PS rack mechanism has failed and pressure cannot be maintained with the leaking seal.
3. You mentioned the steering has started to pull to the left recently. This could be a wheel alignment issue and in that event a fresh wheel alignment would fix the issue. However it could also be a problem with the PS rack mechanism and this is probably more likely the case given that you have other issues with the PS system. If you find the steering pulls to one side while driving the vehicle it might be due to a leaky spool valve in the PS rack that is routing pressure to one side of the PS rack.
4. You have not said how many miles are on your Mazda. However, there are no cheap fixes for these issues and based on these symptoms you may need to have both the PS rack replaced and , if the PS pump is actually failing, the PS pump replaced also. Replacing the PS rack will be expensive.
5. I cannot tell you what the likely under bonnet noise is because it could be from numerous sources, including inside the engine, and you have not indicated where the noise is originating from.
6. If I were you I would be looking to update the vehicle and get into a better one in good condition, with good service records and with less than 60000 miles. A 2004 is an old car now and you will probably need to keep throwing money at it to keep it on the road especially with all the wear and tear that comes with higher mileages.