No, nothing wrong, but often, when trying to troubleshoot a hard-start / n-start condtion, it is faster, easier, cheaper to just replace the carburetor(list price for a new carb is < $20.)
The fuel pump is a plain-simple vacuum-type design:
Vacuum (yellow) operates the internal diaphragm, drawing fuel from the tank (pink) and then out/up (purple) to the inlet fitting on the carburetor. Check for cracks, pinched tube, any other obvious damage. Confirm all tube connections are secure with OEM clamps.