The gasket is usually compressed when the inner part of the drain is attached, creating the seal. If the rubber is decomposed, you can usually find a replacement. They are often tapered to account for a non-vertical tub wall. you must get the taper in the right orientation to create the seal.
If you remove the water, mold, if it exists, will go dormant. if it has damaged the drywall of the ceiling, then you'd have to tear it out and repair anyways. removal of all loose mold and spray with bleach and water will normally kill any spores left.