Your sealed pump basin and the trapped sink drain will both need a vent. They can be connected together 6" or higher above the flood level of the sink. The vent must continue at an up hill grade until it ties into an existing vent or is vented to the outside by itself. It can not turn back down or form any kind of trap before tying into a vent. You must continue the pump basin vent up 6" above the flood level rim of the fixture on the main floor before connecting into that fixture's existing vent.
This vent coming out of the waste stack on a horizontal doesn't have any fixtures draining into it?