Bush ivy is the adult phase of creeping ivy (Hedera) - seedlings start out creeping, with the shrubby, flowering growth appearing years later. To get a new plant that has the bush habit, you have to root it from cuttings. I've read these do not take nearly as well as cuttings of the creeping growth. Another much grown (in suitable climates) ornamental plant that shows this division into two different growth types that are associated with the maturity of the specimen is Lawson cypress (Chamaecyparis lawsoniana). With certain prevalent cultivars of this such as 'Alumii' the tree can easily be seen to be composed of a lower, older part producing cone-less (sterile) shoots and an upper, more recent section bearing differently structured coning (fertile) sprays.

I still think it's Ivy, a plant which is ubiquitous here and with which I am very familiar. I can see some flowering Ivy from where I am sitting right now. Embryonic Ivy fruit, which is what the photo shows, rather than flowers, look quite different from Fatsia fruit. The stems of Fatsia flowers/fruit are also much paler and smoother than those in the photo. Does Fatsia japonica grow in Tacoma? Fatsia leaves are massive and unique so even the briefest description would differentiate it immediately from Ivy if the OP could ask the photographer.

I thought that they looked like oaks, which is good since they don't have as dense a network of surface roots. That will help your garden. if you have water sheeting across the lawn towards the house, you might want to consult with a professional about doing a bit of recontouring of the yard so that the water flows around to the sides or away from the house since a wet foundation isn't great. The azaleas won't do anything to change the drainage.

Maybe stressed is a better word than sick. But going by their size, I’d guess they were grown in a hothouse and some plants react adversely to the change as I’m betting your house is cooler. It doesn’t mean they can’t take cold, just that they respond quickly to sudden change. ALA you don’t overwater and keep in sunniest spot possible, it should recover. Yellowing leaves in this plant w/b a red flag to me and cue to keep a close eye for a bit.