Wow, you got a real mess there. The 2 lower numbered codes couldn't cause the P1562. Not likely the higher numbered code is causing the P0303 especially. Not sure about the relation between the P0174 and P0303 without more research. If #3 cylinder is bank 2 could be the same problem.
P0174Mazda
Lean air/fuel ratio bank 2
Probable Cause
1. Low fuel pressure
2. Large vacuum leak
3. Dirty/defective MAF sensor
4. Engine mechanical condition
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P0303Mazda
Cylinder 3 misfire condition detected
Probable Cause
1. Lean air/fuel ratio
2. Weak ignition system
3. Engine mechanical condition
4. Vacuum leak affecting one cylinder
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P1562Mazda
ECM battery back-up voltage low
Probable Cause
1. Failed ECM fuse
2. Open or short circuit condition
3. Failed ECM