Do we need a gable vent, and in either case, how to vent bathroom fan outside (can it be via the gable)?
Gable venting is not a good idea for your attic. Gable vents work well when there are adequately sized vents on opposite sides of the attic, so air can flow across the whole interior space. This design is impossible in your attic because you only have a gable opening at one end.

Ridge/soffit venting is a good solution for your attic (and more popular than gable venting in new construction for good reasons). The ridge vent allows warm air to rise out of the attic, and the soffit vents supply replacement air from the outdoors. These vents are likely visible from outdoors, but they can be subtle; often there's simply a perforated panel installed in the soffit rather than distinct vents.

Adding a gable vent to your system would make it worse. Replacement air could come in through the gable vent instead of the soffits, and airflow would suffer in the parts of your attic further away from the gable.

From your description of the roof decking, you probably don't have a severe ventilation problem. Signs of that would include mold formation and rot in the roof decking, but your roof decking sounds fine. If you do need to improve ventilation, check your soffit venting. Are there vents serving each rafter bay? Is the path from vent to attic unobstructed? Sometimes vents are blocked by over-eager insulation installers; depending on the situation, you might be able to address the issue by installing plastic/foam baffles designed to ensure a path for air, or simply by cutting away or moving insulation. Improvements to ventilation can definitely help with ice dams, but it's hard to suggest particular improvements for your situation without locations &amp; pictures. In particular, as you mention having a vaulted ceiling, I'd suspect your ice dams have more to do with that roof and its connection to the vented roof. If your ice dam issues are sporadic, consider getting a roof rake and clearing snow buildup in the risk areas; and when you get your roof replaced ensure these areas are thoroughly covered with ice &amp; water membrane under the shingles.

For the bathroom vent, either approach is fine as long as it's within the manufacturer's spec for what your fan can handle.