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Yes, the treatment would be the same. Here's an article you may enjoy:
https://www.gardeningknowhow.com/edible/fruits/nectarines/growing-nectarines-in-containers.htm

They are hardy in your area, and will benefit from that cold. In container, for the first year or two, you will leave it out to go dormant. Once it gets to the coldest part of the year, you can bring it indoors. Put it in the sunniest location possible, or use horticultural lighting to bring it out of dormancy. Once the temperatures stay above freezing, consistently, you can take it outdoors and plant it in ground. You can also choose to keep it in container, but it will be time to transplant to a bigger one, at that point.

Here is an article to help you care for them in container:

https://www.gardeningknowhow.com/edible/fruits/nectarines/growing-nectarines-in-containers.htm

Yes. Here are recommended varieties. Plant them in full sun at least 15 feet from the house.

https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=2346&context=extension_histall

https://extension.tennessee.edu/Morgan/Documents/fruittimetable_SP307D.pdf

There is a way to tell if a tree has died; here's an article about scratch testing: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

Citrus is not generally hardy in zone 5, but you say yours fruited last year? Do you take it inside over winter? Here are some hardy citrus that might fare better:

https://www.gardeningknowhow.com/edible/fruits/citrus/cold-hardy-citrus-trees.htm
https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-4/zone-4-nectarine-trees.htm

There are several blights that can infect fruit trees across multiple genera, so if the soil was not treated before planting these trees, I would say that the same disease that took your apples took these, as well.

I would think about treating the area. but this problem will require constant attention:

https://www.gardeningknowhow.com/plant-problems/disease/fire-blight-remedies-and-symptoms.htm

Unfortunately, This appears to be the start of Fire Blight, or any of the related blights. Likely, the soil remains too wet for too long without adequate chance to dry out, thoroughly, down to about 5 to 8 cm between waterings.

I would treat with a fungicide, but this is going to take some serious management to correct from here.

Here are some articles that will help:

https://www.gardeningknowhow.com/edible/fruits/peach/brown-rot-fungus.htm

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm