Do vegans need omega-3 supplementation? If so, what are good vegan sources and how much do we need?

Depends on diet. Vegans should make sure to get plenty of healthy fats of which omega 3s are part of our requirement for essential fatty acids. Nuts and seeds as well as sea vegetables are good sources. The conversion to dha may be lacking and then dha algae sources would be recommended.
B12 & Iron. Vegans need supplement of vitamin B12 and iron. The sources of vegetable iron cannot be processed by humans ( we do not have the enzymes to metabolize them) so popeyes story with spinach is a fallacy. Fish is probably the most common source of omega 3. Nuts have healthy oils too as well as avocado. Check other answers.
Omega 3 = snake oil. Omega 3 fish oil is the same as snake oil, both are high in omega 3 fatty acids which are extremely fragile. Omega 3 fish/snake oils reduce triglycerides by impairing your liver's ablility to make them. However the oxidative stress caused by fish/snake oil actually raises your LDL cholesterol. Some day we may use the phrase "this is just more fish oil" or "here comes the fish oil salesman".