Q: Is the Mikuni Dual Fuel Pump the replacement part for the rounded dual fuel pump that you usually find on a Rotax 503 engine?
This is not the OEM pump on a Rotax 503, but it will work.
Q: Will this Mikuni dual fuel pump properly feed a 582 ul 99?
Yes it will.
Q: Does this Mikuni dual fuel pump have the weep hole for Rotax engines?
This pump does not have the weep hole. Rotax no longer uses a weep hole on the fuel pump.