Well... of course, as soon as I post this I find a list from the Arbor Day order (or at least, I think it was that year's order). No idea which is which (which of the ones that came in this bundle actually survived), but could the third photo be a young Sargeant Crabapple? That's on the list, as is Eastern Redbud, Washington Hawthorn, dogwood (I know it's not that), Goldenraintree and crapemyrtle (I remember wondering why on earth they were shipping crapemyrtles to New England!!) In theory (meaning assuming they sent what they said they were sending), it should be one of those -- and the crabapple seems like the only one it could be? I'd be floored if they were shipping free Bradford pears (which is what someone on Name that Plant thought it was as well) -- aren't they considered more or less invasive plants in a lot of areas these days? So I'm hoping for Sargeant crabapple since I wouldn't mind having one of those for the birds (means the little guy can stay right where he is now, in the bird/butterfly garden).

Mimosa wilt has been reported in California, notably southern CA, though the lack of characteristic symptoms noted in the OP makes this less likely. I'd avoid any cultural changes that might accelerate the tree's decline. As for planting A. julibrissin anywhere where significant disease problems have been reported, it would be best not to give the tree a prominent location, and to accept that it might have a limited life span (someone living about a half mile away from us had a huge old tree in their front yard that went from magnificent to dead over the span of three years). I have two specimens of "Ernest Wilson" grown from seed started three years ago, planted in two out-of-the-way locations. Both survived -9F this past winter with virtually no damage. There are cultivars i.e. "Flame" and "Union: which are said to be wilt-resistant. As for invasiveness, in my part of Kentucky I don't see self-seeded trees growing along roadsides and in "waste places" as described further south.

Looks to be some sort of alder, Alnus sp. Several alder species are on the list of recommended Cleveland street trees.

Yes. Crabs - and pretty much any crab - are excellent apple pollinators. As long as the bloom times coincide.