They do have an inevitable small number of injuries and fatalities during the banding process, Marko. That being said, banders do
undergo a fair amount of training before they can get a license from US Fish and Wildlife Service and that helps keep the incidence of injury low. Some birds with underlying conditions probably do die, but the percentage of deaths is also very low. In the two sessions here, they've banded over 150 birds. Even one injury or death would be well less than 1% for that many birds and they've had no injuries or deaths at all.
As for after banding, I suppose it's possible that a mate might notice the band. However, birds seem to look for specific characteristics in a possible mate that might indicate it's fitness as a partner. Behavior, plumage condition and color, even song, can be used to signal fitness. I'm thinking that absence or presence of a band wouldn't affect mating preferences as long as it's not influencing the factors that birds have evolved to rely on for making choices. Not sure if they've done any studies specifically on that aspect of it or not, though.
It's probably not possible to get good data on whether the process shortens their lives, either. Even if you can locate a dead bird, determining cause of death after the fact in an old carcass isn't easy, and relating a proximal cause of death due to disease or injury back to the stress from banding would be nigh to impossible. Since most birds likely die from predation and are eaten, there's not much evidence to gather. The best they can do is look at recaptures and try to paint a picture of longevity by how often and for how long they continue to see the same individuals. They do catch many of the same birds each year, often for many years in a row (like that downy woodpecker).