I haven't seen any turkey vultures with white on the head. The description sounds like a crested caracara; if so, that is probably a first state record for NH, since their normal range is south Florida and south Texas. A bird that is much more likely to be in New Hampshire is osprey, a fish-eating eagle. It doesn't have any red on it normally, however. Could the red be blood? Neither bird should be just walking or sitting on the beach for hours. This makes me suspect you are looking at an injured osprey. If you can ascertain that this is the case, it would be good to find a wildlife rehabber who could capture and rehab the bird.

Looks like an Orchard Oriole. Their nests are not as pendant as Baltimore Oriole.

We have been having storms, mostly heavy downpours rather than wind. I do not have a lot of squirrels this year, possibly coyotes ate them. I do have a lot of wrens. Several years ago a wren placed a nest in a bird houser that was attached to the house under cover on my back porch. All was well, eggs hatched, and then one day I saw the parents fluttering around. A garder snake was in the nest. It had climbed the wall somehow. My husband eventually got the snake out of the nest with thongs, but it disrupted the nest materials on its way out. The babies were ready to fly, so we hoped they made it out OK. Never really knew. They were gone. The snake did not seem large enough to eat them. Figures crossed for this next brood.

No, it's an eastern bird. Bewick's would be more appropriate for your area at this time of year, possibly Pacific wren depending on how far south you are in California. Regardless you definitely have a wren! If the bird house is being used, there is probably two birds, the male and female! Congratulations! Having birds chose your yard to raise their babies is quite an honor, in my opinion.